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...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 277; no. 5; pp. 798 - 803
Main Author Ovsyannikov, V. M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 22.12.2023
Springer
Springer Nature B.V
Subjects
Continuity equation
Environmental law
Fluid dynamics
Fluid flow
Helmholtz equations
Incompressible flow
Incompressible fluids
Laws, regulations and rules
Mathematics
Mathematics and Statistics
Wave equations
Euler continuity equation
Cauchy–Helmholtz formulas
76Q05
14C99
Gauss–Ostrogradsky formula
inhomogeneous wave equation
sound generation
self-oscillations
high-order terms
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06888-y