类似普罗迪-塞林标准下兰道方程解的先验估计值

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED Archive for Rational Mechanics and Analysis Pub Date : 2024-05-13 DOI:10.1007/s00205-024-01992-y

R. Alonso, V. Bagland, L. Desvillettes, B. Lods

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引用次数: 0

摘要

在本文中，我们引入了类似普罗迪-塞林（Prodi-Serrin）的标准，这使我们能够为所有经典软势能和维度（d）的空间均匀朗道方程的解提供先验估计。我们的分析包含了维数（d=3）中库仑相互作用的物理情形；这概括了西尔维斯特（Silvestre）的工作（J Differ Equ 262:3034-3055, 2017）。我们的方法是定量的，不需要对非线性抛物方程的精细工具有初步了解。

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A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria

In this paper, we introduce Prodi–Serrin like criteria which enable us to provide a priori estimates for the solutions to the spatially homogeneous Landau equation for all classical soft potentials and dimensions \(d \geqq 3\). The physical case of Coulomb interaction in dimension \(d=3\) is included in our analysis; this generalizes the work of Silvestre (J Differ Equ 262:3034–3055, 2017). Our approach is quantitative and does not require a preliminary knowledge of elaborate tools for nonlinear parabolic equations.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.