玻尔兹曼方程受压力和矩限约束的正则性。

IF 2.6 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-07-02 DOI:10.1007/s00220-025-05356-9

Xavier Fernández-Real, Xavier Ros-Oton, Marvin Weidner

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引用次数: 0

摘要

我们证明了在硬势的情况下，无截断的玻尔兹曼方程的解在某些观测值（质量、压力和合适矩）上满足点界时在L∞上具有一致界。因此，我们导出了所有导数的C∞估计和衰减估计，条件是这些宏观边界。我们的L∞估计在极限s × 1下是一致的，因此我们对朗道方程也恢复了相同的结果。

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Regularity for the Boltzmann Equation Conditional to Pressure and Moment Bounds

We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in \(L^\infty \) in the case of hard potentials. As a consequence, we derive \(C^{\infty }\) estimates and decay estimates for all derivatives, conditional to these macroscopic bounds. Our \(L^\infty \) estimates are uniform in the limit \(s \nearrow 1\) and hence we recover the same results also for the Landau equation.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.