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- W4385962762 abstract "The initial-boundary value problem for the inhomogeneous non-cutoff Boltzmann equation is a long-standing open problem. In this paper, we study the stability and long-time dynamics of the Boltzmann equation near a global Maxwellian without angular cutoff assumption in a general $C^3$ domain $Omega$ (including convex and non-convex cases) with physical boundary conditions: inflow and Maxwell-reflection (including diffuse-reflection) boundary conditions. When the domain $Omega$ is bounded, we obtain the global stability in time, which has an exponential decay rate for the inflow boundary for both hard and soft potentials, and for the Maxwell-reflection boundary for hard potentials. The crucial method is to extend the boundary problem in a general domain to the whole space with velocity regularity, followed by the De Giorgi iteration and the $L^2$--$L^infty$ method. We believe that the current work will have a significant impact on the generation of robust applications for the kinetic equations in bounded domains." @default.
- W4385962762 created "2023-08-18" @default.
- W4385962762 creator A5073755636 @default.
- W4385962762 date "2023-08-01" @default.
- W4385962762 modified "2023-10-16" @default.
- W4385962762 title "The Non-cutoff Boltzmann Equation in General Domains" @default.
- W4385962762 doi "https://doi.org/10.48550/arxiv.2308.00494" @default.
- W4385962762 hasPublicationYear "2023" @default.
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