GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

doi:10.1007/s10473-024-0410-x

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1347-1372.doi: 10.1007/s10473-024-0410-x

GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

Hao Wang

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2023-01-05 出版日期:2024-08-25 发布日期:2024-08-30

GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

Hao Wang

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2023-01-05 Online:2024-08-25 Published:2024-08-30
About author:E-mail: wanghaowd@tsinghua.edu.cn
Supported by:
This research was supported by the NSFC (12301284).

摘要/Abstract

摘要： The Landau equation is studied for hard potential with $-2\leq \gamma\leq1$. Under a perturbation setting, a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space $H^d_xL^2_v(d>\frac{3}{2})$, which extends the results of [11] in the torus domain to the whole space $\mathbb{R}^3_x$. Here we utilize the pseudo-differential calculus to derive our desired result.

关键词: Landau equation, nonlinear energy method, global existence, pseudo-differential calculus

Abstract: The Landau equation is studied for hard potential with $-2\leq \gamma\leq1$. Under a perturbation setting, a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space $H^d_xL^2_v(d>\frac{3}{2})$, which extends the results of [11] in the torus domain to the whole space $\mathbb{R}^3_x$. Here we utilize the pseudo-differential calculus to derive our desired result.

Key words: Landau equation, nonlinear energy method, global existence, pseudo-differential calculus

中图分类号:

35Q84

Hao Wang. GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION[J]. 数学物理学报(英文版), 2024, 44(4): 1347-1372.

Hao Wang. GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION[J]. Acta mathematica scientia,Series B, 2024, 44(4): 1347-1372.

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GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

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