Euler Continuity Equation with High-Order Terms in Time
In this paper, we examine the appearance of high-order terms in the continuity equation for an incompressible fluid obtained by L. Euler in 1752 from the linear Cauchy–Helmholtz equations. Solution of the inhomogeneous wave equation allows one calculate or estimate the intensity of vibrations and se...
Saved in:
| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 277; no. 5; pp. 798 - 803 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
22.12.2023
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-023-06888-y |
Cover
Loading…
| Abstract | In this paper, we examine the appearance of high-order terms in the continuity equation for an incompressible fluid obtained by L. Euler in 1752 from the linear Cauchy–Helmholtz equations. Solution of the inhomogeneous wave equation allows one calculate or estimate the intensity of vibrations and self-oscillations, which are sometimes considered spontaneous. |
|---|---|
| AbstractList | In this paper, we examine the appearance of high-order terms in the continuity equation for an incompressible fluid obtained by L. Euler in 1752 from the linear Cauchy–Helmholtz equations. Solution of the inhomogeneous wave equation allows one calculate or estimate the intensity of vibrations and self-oscillations, which are sometimes considered spontaneous. In this paper, we examine the appearance of high-order terms in the continuity equation for an incompressible fluid obtained by L. Euler in 1752 from the linear Cauchy -- Helmholtz equations. Solution of the inhomogeneous wave equation allows one calculate or estimate the intensity of vibrations and self-oscillations, which are sometimes considered spontaneous. Keywords and phrases: Euler continuity equation, high-order terms, Gauss -- Ostrogradsky formula, Cauchy -- Helmholtz formulas, inhomogeneous wave equation, sound generation, self-oscillations. AMS Subject Classification: 14C99, 76Q05 |
| Audience | Academic |
| Author | Ovsyannikov, V. M. |
| Author_xml | – sequence: 1 givenname: V. M. surname: Ovsyannikov fullname: Ovsyannikov, V. M. email: OvsyannikovVM@yandex.ru organization: Moscow State Academy of Water Transport, Noyabrsk Institute of Oil and Gas — Branch of Tyumen Industrial University |
| BookMark | eNp9kU1LxDAQhoMo-PkHPBU8eYgmmXabHmVZP2BhQddzyKaTGtmmmrRo_73RFWRhkYFMCM8zgXmPyb7vPBJyztkVZ6y8jpxVhaRMAGUTKSUd98gRL0qgsqyK_XRnpaAAZX5IjmN8ZUmaSDgi5WxYY8imne-dH1w_ZrP3Qfeu89mH61-ye9e80EWoE7PE0MbM-WzpWjwlB1avI5799hPyfDtbTu_pfHH3ML2ZUwMiH6lNp14JEAUHViCgLaBagWXIWT0xOQNrBRdC5DmXOZhitUIDUNdGFwJzDifkYjP3LXTvA8ZevXZD8OlLJSoOJRMVm_xRjV6jct52fdCmddGom1KySlTAZaLoDqpBj0Gv0z6tS89b_NUOPlWNrTM7hcstITE9fvaNHmJUD0-P26zYsCZ0MQa06i24VodRcaa-M1WbTFXKVP1kqsYkwUaKCfYNhr9t_GN9AWynogo |
| Cites_doi | 10.1007/978-3-642-00292-2 10.1098/rspa.1952.0060 10.1098/rspa.1954.0049 |
| ContentType | Journal Article |
| Copyright | Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. COPYRIGHT 2023 Springer |
| Copyright_xml | – notice: Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: COPYRIGHT 2023 Springer |
| DBID | AAYXX CITATION ISR |
| DOI | 10.1007/s10958-023-06888-y |
| DatabaseName | CrossRef Gale In Context: Science |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1573-8795 |
| EndPage | 803 |
| ExternalDocumentID | A780929318 10_1007_s10958_023_06888_y |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 1N0 1SB 2.D 29L 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 642 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACUHS ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AZFZN B-. B0M BA0 BAPOH BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EAD EAP EAS EBLON EBS EIOEI EJD EMK EPL ESBYG ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG6 HMJXF HQYDN HRMNR HVGLF HZ~ IAO IEA IHE IJ- IKXTQ IOF ISR ITC IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P9R PF0 PT4 PT5 QOK QOS R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 XU3 YLTOR Z7R Z7U Z7X Z7Z Z81 Z83 Z86 Z88 Z8M Z8R Z8T Z8W Z92 ZMTXR ZWQNP ~8M ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION AEIIB ABRTQ |
| ID | FETCH-LOGICAL-c324y-f324ab23251305e3ef539b3f0e10d6c403ff21222441843c5bbec33ddca52e413 |
| IEDL.DBID | U2A |
| ISSN | 1072-3374 |
| IngestDate | Fri Jul 25 11:04:15 EDT 2025 Tue Jun 17 21:59:40 EDT 2025 Fri Jun 13 00:00:44 EDT 2025 Tue Jun 10 20:55:58 EDT 2025 Fri Jun 27 05:17:29 EDT 2025 Tue Jul 01 01:42:25 EDT 2025 Fri Feb 21 02:41:26 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Euler continuity equation Cauchy–Helmholtz formulas 76Q05 14C99 Gauss–Ostrogradsky formula inhomogeneous wave equation sound generation self-oscillations high-order terms |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c324y-f324ab23251305e3ef539b3f0e10d6c403ff21222441843c5bbec33ddca52e413 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2913702906 |
| PQPubID | 2043545 |
| PageCount | 6 |
| ParticipantIDs | proquest_journals_2913702906 gale_infotracmisc_A780929318 gale_infotracgeneralonefile_A780929318 gale_infotracacademiconefile_A780929318 gale_incontextgauss_ISR_A780929318 crossref_primary_10_1007_s10958_023_06888_y springer_journals_10_1007_s10958_023_06888_y |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20231222 |
| PublicationDateYYYYMMDD | 2023-12-22 |
| PublicationDate_xml | – month: 12 year: 2023 text: 20231222 day: 22 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: New York |
| PublicationTitle | Journal of mathematical sciences (New York, N.Y.) |
| PublicationTitleAbbrev | J Math Sci |
| PublicationYear | 2023 |
| Publisher | Springer International Publishing Springer Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer – name: Springer Nature B.V |
| References | LighthillMJOn sound generated aerodynamically. II. Turbulence a source of soundProc. Roy. Soc. Lond. Ser. A19542221326151510.1098/rspa.1954.0049 V. M. Ovsyannikov, “Finite-difference form of the continuity equation with account of shift deformations,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 16 [in Russian], Moscow (2007). V. M. Ovsyannikov, “History of the derivation of the continuity equation,” in: Proc. XI All-Russian Conf. “Fundamental Problems of Theoretic and Applied Mechanics” (Kazan, August 20–24, 2015) [in Russian], Kazan (2015), pp. 2823–2824. V. M. Ovsyannikov, “Zhukovsky deformation ellipsoid with account of second-order terms,” Inzh. Zh. Nauka Innov., No. 5 (77) (2018), pp. 1–11. ElizarovaTGQuasi-Gas Dynamic Equations2009BerlinSpringer10.1007/978-3-642-00292-2 V. M. Ovsyannikov, “Calculations of the occurrence of fluid motions in pipelines,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 5, 158–160 (1981). V. M. Ovsyannikov, “Introduction to axiomatic fluid mechanics based on basic fluid experiments,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 15 [in Russian], Moscow (2006), pp. 19–51. V. M. Ovsyannikov, “Using the Leibniz and Newton axioms of the theory of infinitesimal quantities for deriving the wave differential equation,” in: Proc. Int. Conf. on Differential Equations and Dynamic Systems (Suzdal, July 6–11, 2018) [in Russian], Suzdal (2018), pp. 155–156. LighthillMJOn sound generated aerodynamically. I. General theoryProc. Roy. Soc. Lond. Ser. A19522115645874745910.1098/rspa.1952.0060 T. A. Koppel and U. R. Liiv, “Experimental study of the occurrence of fluid motions in pipelines,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 6, 78–85 (1977). V. A. Bubnov, “Kinematics of Fluid Particles,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 7 [in Russian], Prometei, Moscow (1999), pp. 11–29. L. Euler, Commentationes Mechanicae ad Theoriam Corporum Fluidorum Pertinentes (Truesdell C. A., ed.), Orell Fuessli, Zürich (1954). OvsyannikovVMComparison of additional second-order terms in finite-difference Euler equations and regularized fluid dynamics equationsZh. Vychisl. Mat. Mat. Fiz.20175758768803661123 OvsyannikovVMWave Formation and the Finite-Difference Continuity Equation2017MoscowSputnik+[in Russian] V. A. Bubnov, “Physical Principles of Hydrodynamic Motions,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 4 [in Russian], Prometei, Moscow (1997), pp. 206–269. EulerLGeneral laws of fluid motionsMekh. Zhidk. Gaza199962654 LandauLDLifshitsEMHydrodynamics1986MoscowNauka[in Russian] OvsyannikovVMLocal Differential Nonconservation and Integral Conservation in Gas Dynamics2017MoscowSputnik+[in Russian] V. M. Ovsyannikov, “Landau–Lifshits vibrator in equations of gas dynamics,” Inzh. Zh. Nauka Innov., No. 4 (76) (2018), pp. 1–8. TG Elizarova (6888_CR3) 2009 MJ Lighthill (6888_CR8) 1952; 211 MJ Lighthill (6888_CR9) 1954; 222 6888_CR19 6888_CR5 6888_CR18 6888_CR17 L Euler (6888_CR4) 1999; 6 6888_CR6 6888_CR1 6888_CR2 VM Ovsyannikov (6888_CR15) 2017 VM Ovsyannikov (6888_CR16) 2017 6888_CR13 6888_CR12 VM Ovsyannikov (6888_CR14) 2017; 57 6888_CR11 6888_CR10 LD Landau (6888_CR7) 1986 |
| References_xml | – reference: V. M. Ovsyannikov, “Introduction to axiomatic fluid mechanics based on basic fluid experiments,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 15 [in Russian], Moscow (2006), pp. 19–51. – reference: OvsyannikovVMWave Formation and the Finite-Difference Continuity Equation2017MoscowSputnik+[in Russian] – reference: OvsyannikovVMComparison of additional second-order terms in finite-difference Euler equations and regularized fluid dynamics equationsZh. Vychisl. Mat. Mat. Fiz.20175758768803661123 – reference: EulerLGeneral laws of fluid motionsMekh. Zhidk. Gaza199962654 – reference: LighthillMJOn sound generated aerodynamically. II. Turbulence a source of soundProc. Roy. Soc. Lond. Ser. A19542221326151510.1098/rspa.1954.0049 – reference: ElizarovaTGQuasi-Gas Dynamic Equations2009BerlinSpringer10.1007/978-3-642-00292-2 – reference: LighthillMJOn sound generated aerodynamically. I. General theoryProc. Roy. Soc. Lond. Ser. A19522115645874745910.1098/rspa.1952.0060 – reference: V. M. Ovsyannikov, “Using the Leibniz and Newton axioms of the theory of infinitesimal quantities for deriving the wave differential equation,” in: Proc. Int. Conf. on Differential Equations and Dynamic Systems (Suzdal, July 6–11, 2018) [in Russian], Suzdal (2018), pp. 155–156. – reference: L. Euler, Commentationes Mechanicae ad Theoriam Corporum Fluidorum Pertinentes (Truesdell C. A., ed.), Orell Fuessli, Zürich (1954). – reference: T. A. Koppel and U. R. Liiv, “Experimental study of the occurrence of fluid motions in pipelines,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 6, 78–85 (1977). – reference: OvsyannikovVMLocal Differential Nonconservation and Integral Conservation in Gas Dynamics2017MoscowSputnik+[in Russian] – reference: LandauLDLifshitsEMHydrodynamics1986MoscowNauka[in Russian] – reference: V. M. Ovsyannikov, “Landau–Lifshits vibrator in equations of gas dynamics,” Inzh. Zh. Nauka Innov., No. 4 (76) (2018), pp. 1–8. – reference: V. M. Ovsyannikov, “Calculations of the occurrence of fluid motions in pipelines,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 5, 158–160 (1981). – reference: V. A. Bubnov, “Physical Principles of Hydrodynamic Motions,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 4 [in Russian], Prometei, Moscow (1997), pp. 206–269. – reference: V. A. Bubnov, “Kinematics of Fluid Particles,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 7 [in Russian], Prometei, Moscow (1999), pp. 11–29. – reference: V. M. Ovsyannikov, “Zhukovsky deformation ellipsoid with account of second-order terms,” Inzh. Zh. Nauka Innov., No. 5 (77) (2018), pp. 1–11. – reference: V. M. Ovsyannikov, “Finite-difference form of the continuity equation with account of shift deformations,” in: Problems of Axiomatics in Fluid Dynamics. Vol. 16 [in Russian], Moscow (2007). – reference: V. M. Ovsyannikov, “History of the derivation of the continuity equation,” in: Proc. XI All-Russian Conf. “Fundamental Problems of Theoretic and Applied Mechanics” (Kazan, August 20–24, 2015) [in Russian], Kazan (2015), pp. 2823–2824. – volume-title: Quasi-Gas Dynamic Equations year: 2009 ident: 6888_CR3 doi: 10.1007/978-3-642-00292-2 – volume-title: Wave Formation and the Finite-Difference Continuity Equation year: 2017 ident: 6888_CR15 – volume: 57 start-page: 876 issue: 5 year: 2017 ident: 6888_CR14 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – ident: 6888_CR13 – volume: 211 start-page: 564 year: 1952 ident: 6888_CR8 publication-title: Proc. Roy. Soc. Lond. Ser. A doi: 10.1098/rspa.1952.0060 – ident: 6888_CR2 – volume: 6 start-page: 26 year: 1999 ident: 6888_CR4 publication-title: Mekh. Zhidk. Gaza – volume-title: Hydrodynamics year: 1986 ident: 6888_CR7 – ident: 6888_CR5 – ident: 6888_CR6 – ident: 6888_CR19 – ident: 6888_CR1 – ident: 6888_CR17 – ident: 6888_CR18 – volume: 222 start-page: 1 year: 1954 ident: 6888_CR9 publication-title: Proc. Roy. Soc. Lond. Ser. A doi: 10.1098/rspa.1954.0049 – ident: 6888_CR11 – volume-title: Local Differential Nonconservation and Integral Conservation in Gas Dynamics year: 2017 ident: 6888_CR16 – ident: 6888_CR12 – ident: 6888_CR10 |
| SSID | ssj0007683 |
| Score | 2.3013709 |
| Snippet | In this paper, we examine the appearance of high-order terms in the continuity equation for an incompressible fluid obtained by L. Euler in 1752 from the... |
| SourceID | proquest gale crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 798 |
| SubjectTerms | Continuity equation Environmental law Fluid dynamics Fluid flow Helmholtz equations Incompressible flow Incompressible fluids Laws, regulations and rules Mathematics Mathematics and Statistics Wave equations |
| Title | Euler Continuity Equation with High-Order Terms in Time |
| URI | https://link.springer.com/article/10.1007/s10958-023-06888-y https://www.proquest.com/docview/2913702906 |
| Volume | 277 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3JTsNADLWgvcABsYqwVCOE4AAjpZlJkx5baNkESEAlOI2yzFSVUICmPfTvsbMAYTlwSQ6xRomd8XNi-xlg36cY229GvBVTSw7agZKEkkvfGEoEhbah3uHrm9b5QF4-uo9FU1haVruXKcnMU39pdmu7PkeMyQal-Hw2D3UXv92pkG_gdD78LwbQeVm953AhPFm0yvy-RgWOvjvlH9nRDHT6y7BURIusk5t3BeZ0sgqL1x9Uq-kaeL3psx4zYpkaJVOMqVnvLafvZvSPlVEhB78lgk32gF44ZaOEUd_HOgz6vYeTc15MQ-ARBj0zbvAYhBgAuQg7rhbauKIdCmPrph23ImkLYxCHEJIlzXCJ3BDNI0QcR4HraMSqDaglL4neBKZtSYP4Qhm0bBnLMJBhjFhNy2sTt30LjkqlqNec9EJ90huTChWqUGUqVDML9khvitgkEipXGQbTNFUX93eq4_k2xl_oNyw4LITMy2QcREFR_Y83RARUFcmDiuQwp9_-TXCnIoj7IqpeLu2oin2ZKqfdFJ5NFPcWHJe2_bz890Nu_U98GxZoLj3VvTjODtQm46nexehlEjag3umedvt0Pnu66jWyl_cdHAHlxg |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT-MwEB5BOQCH5S26yy4WQnAAozR2mvRYrQrlUZCgleBkxYmNEChA0xy6v56ZJoENjwOXXDyynBl75ktm5jPAdkAYO2hEvBlTSw7agZKEksvAWkoEacdS73DvvNkdyJNr77poCkvLavcyJTnx1P81u7W8gGOMmVyUEvDxNMxI_AaXNZhpH92cdl49MELovLDed7kQviyaZT6fpRKQ3rvlD_nRSdg5XIBBueC82uT-IBvpg-jfOy7H777RIvwocChr5xtnCaZMsgzzvVcS13QF_E72YIaM-KvukgzROus858TgjP7eMioR4RdE3cn66N9Tdpcw6ihZhcFhp_-3y4t7FniEcGrMLT5DjdDKw4DmGWGsJ1paWMc0nLgZSUdYixEOg72k22EiT6PhhYjjKPRcg1FwDWrJY2LWgRlH0hV_WoZNR8ZSh1LHiAJoemPjVlCHvVLZ6imn01BvxMmkDoXqUBN1qHEdtsgeingqEiqEuQ2zNFXHV5eq7QcOIjv0SHXYLYTs42gYRmHRV4ALImqriuRORfI2J_b-THCjIognLqoOl_tDFSc-VW6rIXyHyPPrsF-a-23465f8-T3xTZjt9ntn6uz4_PQXzLm0exoud90NqI2GmfmNGGmk_xRH4gXDRAMN |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwEB6VRUJwKFBasS0PC1VwoIZs7Gyyx1W7y5tWPKTtyYoTGyFQoJvksPx6ZjYJEAoHxCUXjyx7PJ75FM98A_A9IIwdtCLejqkkB8-BHgkll4G19BCkHUu1w0fH7d1zuT_wBk-q-MfZ7tWTZFHTQCxNSbZ9G9vtJ4VvHS_gGG_GTVMCPpqASUnk7A2Y7O78Peg9eGOE00WSve9yIXxZFs68PEstOD130f-9lY5DUH8WwmrxRebJ1Vae6a3o7hmv43t2NwcfS3zKuoVBzcMHk3yCmaMHctd0Afxefm2GjHitLpMcUTzr_SsIwxn91WWUOsJ_E6UnO0O_n7LLhFGlyWc47_fOfu7ysv8CjxBmjbjFb6gRcnkY6DwjjPVERwvrmJYTtyPpCGsx8iEIkNQ1JvI0GoQQcRyFnmswOn6BRnKTmEVgxpHU-k_LsO3IWOpQ6hjRAU1vbNwJmrBZKV7dFjQb6pFQmdShUB1qrA41asIanY0i_oqEEmQuwjxN1d7pier6gYOIDz1VEzZKIXuTDcMoLOsNcEFEeVWTXK9JXhSE3y8JLtUE8SZG9eHKVlTpCVLldlrCd4hUvwk_qqN_HH59k1_fJr4KU39-9dXh3vHBN5h2yXhaLnfdJWhkw9wsI3TK9Ep5O-4B4NYL8Q |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=EULER+CONTINUITY+EQUATION+WITH+HIGH-ORDER+TERMS+IN+TIME&rft.jtitle=Journal+of+mathematical+sciences+%28New+York%2C+N.Y.%29&rft.au=Ovsyannikov%2C+V.+M&rft.date=2023-12-22&rft.pub=Springer&rft.issn=1072-3374&rft.volume=277&rft.issue=5&rft.spage=798&rft_id=info:doi/10.1007%2Fs10958-023-06888-y&rft.externalDBID=ISR&rft.externalDocID=A780929318 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1072-3374&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1072-3374&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1072-3374&client=summon |