Abstract
AbstractWe consider the Boltzmann equation in a convex domain with a non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belonging to $$W^{1,p}_x$$
W
x
1
,
p
for any $$p<3$$
p
<
3
. We prove that the unsteady solution converges to the steady solution in the same Sobolev space exponentially quickly as $$t \rightarrow \infty $$
t
→
∞
.
Funder
Division of Mathematical Sciences
National Science Foundation
National Natural Science Foundation of China
National Research Foundation of Korea
Research Grants Council, University Grants Committee
Publisher
Springer Science and Business Media LLC
Reference16 articles.
1. Cao, Y., Kim, C., Lee, D.: Global Strong Solutions of the Vlasov-Poisson-Boltzmann System in Bounded Domains. Arch. Ration. Mech. Anal. 1, 1–104, 2019
2. Chen, H.: Regularity of Boltzmann Equation with Cercignani–Lampis Boundary in Convex Domain. SIAM J. Math. Anal. 54, 3316–3378, 2022
3. Chen, H., Kim, C.: Regularity of stationary Boltzmann equation in convex domains. Arch. Ration. Mech. Anal. 244, 1099–1222, 2022
4. Chen, H., Kim, C., Li, Q.: Local Well–Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition. J. Stat. Phys. 179, 535–631, 2020
5. Chen, I.-K., Hsia, C.-H., Kawagoe, D.: Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain. In: Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 36, pp. 745–782. Elsevier, 2019.