On local well-posedness of problems with characteristic free boundary for hyperbolic systems of conservation laws Full article
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Russian Mathematical Surveys
ISSN: 0036-0279 , E-ISSN: 1468-4829 |
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| Output data | Year: 2024, Volume: 79, Number: 2, Pages: 325-360 Pages count : 36 DOI: 10.4213/rm10150e | ||
| Tags | hyperbolic system of conservation laws, free boundary problem, characteristic boundary, local existence and uniqueness theorem, loss of derivatives in a priori estimates, non-ellipticity of the boundary symbol, secondary symmetrization, tame estimates, Nash–Moser method. | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0008 |
Abstract:
The proof of the local-in-time existence and uniqueness of a smooth solution to a free boundary problem for a hyperbolic system of conservation laws has some additional difficulties if the free boundary is a characteristic of this system. They are connected with the loss of control of the normal derivatives and the possible non-ellipticity of the symbol of the free boundary. Another peculiarity of problems with characteristic free boundary is that usually a loss of derivatives of the coefficients and source terms occurs in a priori estimates for the corresponding linearized problems. Moreover, the boundary conditions in the linearized problem can be non-dissipative, which makes it difficult to use the energy method. We describe methods for overcoming these difficulties. Our main examples are free boundary problems for Euler’s equations and the equations of ideal compressible magnetohydrodynamics, for which we review the results on their local well-posedness. Bibliography: 61 titles.
Cite:
Trakhinin Y.L.
On local well-posedness of problems with characteristic free boundary for hyperbolic systems of conservation laws
Russian Mathematical Surveys. 2024. V.79. N2. P.325-360. DOI: 10.4213/rm10150e WOS Scopus РИНЦ OpenAlex
On local well-posedness of problems with characteristic free boundary for hyperbolic systems of conservation laws
Russian Mathematical Surveys. 2024. V.79. N2. P.325-360. DOI: 10.4213/rm10150e WOS Scopus РИНЦ OpenAlex
Original:
Трахинин Ю.Л.
О локальной корректности задач с характеристическими свободными границами для гиперболических систем законов сохранения
Успехи математических наук. 2024. Т.79. №2(476). С.145-182. DOI: 10.4213/rm10150 РИНЦ OpenAlex
О локальной корректности задач с характеристическими свободными границами для гиперболических систем законов сохранения
Успехи математических наук. 2024. Т.79. №2(476). С.145-182. DOI: 10.4213/rm10150 РИНЦ OpenAlex
Dates:
| Submitted: | Sep 14, 2023 |
| Published print: | Aug 12, 2024 |
| Published online: | Aug 12, 2024 |
Identifiers:
| Web of science: | WOS:001306112700003 |
| Scopus: | 2-s2.0-85203720429 |
| Elibrary: | 73441252 |
| OpenAlex: | W4401464595 |