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Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions

The author was supported by the 150th Anniversary Postdoctoral Mobility Grant of the London Mathematical Society and by the Division of Applied Mathematics of Brown University
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  • We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo [21] in $L_{x,v}^\infty \left( {{{\left( {1 + |v|} \right)}^\beta }{e^{|v{|^2}/4}}} \right)$, we prove existence, uniqueness, continuity and positivity of solutions for less restrictive weights in the velocity variable; namely, polynomials and stretch exponentials. The methods developed here are constructive.

    Mathematics Subject Classification: Primary: 35Q20, 35B20; Secondary: 76P05.

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