Asymptotics and scattering for wave Klein-Gordon systems
We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified version of global existence based on LeFloch-Ma, and then derive...
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| Published in | Communications in partial differential equations Vol. 48; no. 9; pp. 1102 - 1147 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
02.09.2023
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0360-5302 1532-4133 |
| DOI | 10.1080/03605302.2023.2263205 |
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| Abstract | We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified version of global existence based on LeFloch-Ma, and then derive the asymptotic behavior of the system. The asymptotics of the Klein-Gordon field consist of a modified phase times a homogeneous function, and the asymptotics of the wave equation consist of a radiation field in the wave zone and an interior homogeneous solution coupled to the Klein-Gordon asymptotics. We then consider the inverse problem, the scattering from infinity. We show that given the type of asymptotic behavior at infinity, there exist solutions of the system that present the exact same behavior. |
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| AbstractList | We study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified version of global existence based on LeFloch-Ma, and then derive the asymptotic behavior of the system. The asymptotics of the Klein-Gordon field consist of a modified phase times a homogeneous function, and the asymptotics of the wave equation consist of a radiation field in the wave zone and an interior homogeneous solution coupled to the Klein-Gordon asymptotics. We then consider the inverse problem, the scattering from infinity. We show that given the type of asymptotic behavior at infinity, there exist solutions of the system that present the exact same behavior. |
| Author | Lindblad, Hans Chen, Xuantao |
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| References_xml | – volume-title: Radiation field for Einstein vacuum equations. ProQuest LLC year: 2010 ident: e_1_3_2_28_1 – ident: e_1_3_2_35_1 doi: 10.1142/9427 – volume-title: The Einstein-Klein-Gordon Coupled System: Global Stability of the Minkowski Solution:(AMS-213) year: 2022 ident: e_1_3_2_6_1 – ident: e_1_3_2_26_1 doi: 10.1090/S0002-9947-2015-06061-9 – ident: e_1_3_2_32_1 doi: 10.1007/s00028-023-00925-8 – ident: e_1_3_2_27_1 doi: 10.1353/ajm.2015.0033 – start-page: 109 year: 2006 ident: e_1_3_2_23_1 article-title: Global stability for charged-scalar fields on Minkowski space publication-title: IMRP Int. Math. Res. Pap. – ident: e_1_3_2_33_1 doi: 10.1088/1361-6382/acde31 – ident: e_1_3_2_21_1 doi: 10.1007/s00220-021-03989-0 – ident: e_1_3_2_22_1 doi: 10.1007/s00220-021-03989-0 – ident: e_1_3_2_15_1 doi: 10.1137/20M1323722 – ident: e_1_3_2_25_1 doi: 10.1007/s00220-021-04105-y – ident: e_1_3_2_13_1 doi: 10.1090/S0002-9947-2014-06455-6 – ident: e_1_3_2_18_1 – ident: e_1_3_2_10_1 doi: 10.1016/S0012-9593(00)01059-4 – ident: e_1_3_2_30_1 doi: 10.1002/cpa.3160380512 – ident: e_1_3_2_4_1 doi: 10.1016/S1631-073X(03)00231-0 – volume-title: Lectures on Nonlinear Hyperbolic Differential Equations year: 1997 ident: e_1_3_2_8_1 – ident: e_1_3_2_14_1 doi: 10.1090/tran/6478 – ident: e_1_3_2_16_1 doi: 10.1007/s00205-021-01675-y – ident: e_1_3_2_24_1 doi: 10.1007/s00220-019-03285-y – ident: e_1_3_2_11_1 doi: 10.1016/j.ansens.2006.01.001 – ident: e_1_3_2_12_1 doi: 10.1007/s11005-005-0021-y – ident: e_1_3_2_19_1 doi: 10.1142/S0219891605000385 – ident: e_1_3_2_5_1 doi: 10.1142/10730 – ident: e_1_3_2_20_1 – year: 2020 ident: e_1_3_2_17_1 article-title: On modified scattering for 1D quadratic Klein-Gordon equations with non-generic potentials publication-title: to appear in IMRN – ident: e_1_3_2_31_1 – ident: e_1_3_2_2_1 doi: 10.1007/s00220-015-2549-8 – ident: e_1_3_2_29_1 doi: 10.1016/j.aim.2023.109042 – ident: e_1_3_2_34_1 doi: 10.1002/cpa.21864 – ident: e_1_3_2_36_1 doi: 10.1007/s40818-021-00092-4 – ident: e_1_3_2_9_1 doi: 10.1007/s00220-017-2876-z – ident: e_1_3_2_3_1 doi: 10.1007/s10114-019-8413-6 – ident: e_1_3_2_7_1 doi: 10.1098/rspa.1962.0162 |
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| SubjectTerms | Asymptotic properties Asymptotics Infinity Inverse problems Klein-Gordon equation Scattering Scattering from infinity Wave equations Wave-Klein-Gordon systems |
| Title | Asymptotics and scattering for wave Klein-Gordon systems |
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