| Abstract: |
| In this talk, we will investigate the existence of the non-cutoff Boltzmann equation near a global Maxwellian in a general $C^3$ bounded domain $\Omega$. This includes convex and non-convex cases with inflow or Maxwell reflection boundary conditions. We obtain global-in-time existence, which has an exponential decay rate for both hard and soft potentials. The crucial method is to extend the boundary problem in a bounded domain to the whole space without regular velocity dissipation and to construct an extra damping from the advection operator, followed by the De Giorgi iteration and the $L^2$--$L^\infty$ method. |
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