一维Euler–Boltzmann方程光滑解的爆破和非全局存在性

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2023-03-01 DOI:10.1142/s0219891623500030

Jianwei Dong, YI-JIE Meng

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引用次数: 0

摘要

在本文中，我们研究了辐射流体力学的一维Euler–Boltzmann方程光滑解的爆破和非全局存在性。首先，我们通过去除限制条件，改进了[P.Jiang和Y.G.Wang，一维非相对论辐射流体动力学方程的初边值问题和奇点的形成，J.Hyperbolic Differential equations 9（2012）711-738]中关于大初始数据的半线上[公式：见正文]的Blow-up结果。接下来，我们通过引入新的动量权重，在半直线[公式：见正文]上获得了一个新的放大结果。最后，通过引入一些新的平均量，我们给出了区间[公式：见正文]上具有真空的一维Euler–Boltzmann方程光滑解的两个非全局存在性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Blowup and non-global existence of smooth solutions to the one-dimensional Euler–Boltzmann equations

In this paper, we study the blowup and non-global existence of smooth solutions to the one-dimensional Euler–Boltzmann equations of radiation hydrodynamics. First, we improve the blowup result in [P. Jiang and Y. G. Wang, Initial-boundary value problems and formation of singularities for one-dimensional non-relativistic radiation hydrodynamic equations, J. Hyperbolic Differential Equations 9 (2012) 711–738] on the half line [Formula: see text] for large initial data by removing a restrict condition. Next, we obtain a new blowup result on the half line [Formula: see text] by introducing a new momentum weight. Finally, we present two non-global existence results for the smooth solutions to the one-dimensional Euler–Boltzmann equations with vacuum on the interval [Formula: see text] by introducing some new average quantities.

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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.