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arXiv · 2304.06933

Gradient Decay in the Boltzmann theory of Non-isothermal boundary

Hongxu Chen·Chanwoo Kim
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Abstract

We consider the Boltzmann equation in convex domain with non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belong to $W^{1,p}_x$ for any $p<3$. We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially fast as $t \rightarrow \infty$.

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Hongxu Chen, Chanwoo Kim. 2023-04-14. Gradient Decay in the Boltzmann theory of Non-isothermal boundary. https://arxiv.org/abs/2304.06933

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