GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

doi:10.1007/s10473-024-0410-x

Abstract

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

CLC Number:

35Q84

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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