存在稀疏波时欧拉方程的初边值问题

IF 0.5 4区 数学 Q4 MATHEMATICS, APPLIED
Dening Li
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引用次数: 0

摘要

研究了一般非等熵三维欧拉方程的初边值问题,该方程具有经典意义上不相容但“稀疏相容”的数据。我们证明了这些数据也是无限阶稀疏相容的,并且初始边值问题具有包含稀疏波的分段光滑解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the initial-boundary value problem for the Euler equations in presence of a rarefaction wave
We study the initial-boundary value problem for the general non-isentropic 3D Euler equations with data which are incompatible in the classical sense, but are “rarefaction-compatible”. We show that such data are also rarefaction-compatible of infinite order and the initial-boundary value problem has a piece-wise smooth solution containing a rarefaction wave.
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来源期刊
Journal of Hyperbolic Differential Equations
Journal of Hyperbolic Differential Equations 数学-物理:数学物理
CiteScore
1.10
自引率
0.00%
发文量
15
审稿时长
24 months
期刊介绍: This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.
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