渐近平坦空间中Maxwell和spin-2场的类空边界

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2021-07-19 DOI:10.1142/s0219891621500119

Qing Han, Lin Zhang

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引用次数: 0

摘要

我们研究了Bondi–Sachs坐标系中与渐近平坦洛伦兹度量相关的Maxwell方程和自旋2场方程。我们考虑混合边值/初值问题，其中初始数据被施加在零超曲面上，边值被规定在类时间超曲面上。我们建立了解的Sobolev[公式：见正文]时空估计及其在零无穷大处的渐近展开式。

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On the null-timelike boundary for Maxwell and spin-2 fields in asymptotically flat spaces

We study the Maxwell equation and the spin-2 field equation in Bondi–Sachs coordinates associated with an asymptotically flat Lorentzian metric. We consider the mixed boundary/initial value problem, where the initial data are imposed on a null hypersurface and a boundary value is prescribed on a timelike hypersurface. We establish Sobolev [Formula: see text] space-time estimates for solutions and their asymptotic expansions at the null infinity.

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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.