The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2019-06-19 DOI:10.1142/s0219891621500041

vS'arka Nevcasov'a, X. Blanc, R. Danchin, B. Ducomet, andvs Nevcasov'a

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引用次数: 6

Abstract

We consider the Cauchy problem for the barotropic Euler system coupled to Helmholtz or Poisson equations, in the whole space. We assume that the initial density is small enough, and that the initial velocity is close to some reference vector field [Formula: see text] such that the spectrum of [Formula: see text] is positive and bounded away from zero. We prove the existence of a global unique solution with (fractional) Sobolev regularity, and algebraic time decay estimates. Our work extends Grassin and Serre’s papers [Existence de solutions globales et régulières aux équations d’Euler pour un gaz parfait isentropique, C. R. Acad. Sci. Paris Sér. I 325 (1997) 721–726, 1997; Global smooth solutions to Euler equations for a perfect gas, Indiana Univ. Math. J. 47 (1998) 1397–1432; Solutions classiques globales des équations d’Euler pour un fluide parfait compressible, Ann. Inst. Fourier Grenoble 47 (1997) 139–159] dedicated to the compressible Euler system without coupling and with integer regularity exponents.

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具有Poisson或Helmholtz耦合的可压缩Euler系统的全局存在性问题

我们考虑了在整个空间中耦合到亥姆霍兹方程或泊松方程的正压欧拉系统的柯西问题。我们假设初始密度足够小，并且初始速度接近某个参考向量场[公式:见文本]，使得[公式:见文本]的谱为正，并且有界远离零。我们证明了一个具有(分数)Sobolev正则性和代数时间衰减估计的全局唯一解的存在性。我们的工作扩展了Grassin和Serre的论文[存在de solutions globales et r guli res aux parfait isentropique, C. R. acacad . Sci]。巴黎爵士。I 325 (1997) 721-726, 1997;完美气体欧拉方程的全局光滑解，印第安纳大学数学。J. 47 (1998) 1397-1432;非流体部件可压缩，安。研究所。傅里叶格勒诺布尔47(1997)139-159]致力于无耦合和具有整数正则指数的可压缩欧拉系统。

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

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.