Solving Linearized Landau Equation Pointwisely

2017/09/04 by Haitao Wang, Wang, Haitao, Kung-Chien Wu +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1709.00839

openalex publication_date 2017/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the pointwise (in the space and time variables) behavior of the linearized Landau equation for hard and moderately soft potentials. The solution has very clear description in the (x,t)-variables, including large time behavior and asymptotic behavior. More precisely, we obtain the pointwise fluid structure inside finite Mach number region, and exponential or sub-exponential decay, depending on interactions between particles, in the space variable outside finite Mach number region. The spectrum analysis, regularization effect and refined weighted energy estimate play important roles in this paper.

Citations

• On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation

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