Regularity in kinetic formulations via averaging lemmas
Regularity in kinetic formulations via averaging lemmas
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通过平均引理得出动力学公式的规律性
DOI：
10.1051/cocv:2002033
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
B. Perthame
中科院分区：
文献类型：
--
作者：
P. Jabin;B. Perthame
我们提出了一类新的平均引理直接动机的问题，不同的非线性方程或变分问题，承认一个动力学制定的正则性。特别是，它们改进了等熵气体动力学中γ = 3系统或微磁薄膜中的某些变分问题的已知正则性。它们还允许直接获得多维标量守恒律中最著名的正则化效应。这里的新成分是使用速度正则性来求解所考虑的输运方程。证明的方法是基于傅立叶空间的密度分解，结合真实的插值的K -方法。
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity regularity for the solution to the transport equation under consideration. The method of proof is based on a decomposition of the density in Fourier space, combined with the K -method of real interpolation.