On C² solution of the free-transport equation in a disk

2021/12/03 by Gyounghun Ko, Donghyun Lee, Ko, Gyounghun +1 · 1 citation
Mathematics · #35B65 #35F16 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.01744

openalex publication_date 2021/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The free transport operator of probability density function f(t,x,v) is one the most fundamental operator which is widely used in many areas of PDE theory including kinetic theory, in particular. When it comes to general boundary problems in kinetic theory, however, it is well-known that high order regularity is very hard to obtain in general. In this paper, we study the free transport equation in a disk with the specular boundary condition. We obtain initial-boundary compatibility conditions for C¹_t,x,v and C²_t,x,v regularity of the solution. We also provide regularity estimates.

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