TY - JOUR
T1 - The Navier–Stokes–Vlasov–Fokker–Planck System in Bounded Domains
AU - Li, Hailiang
AU - Liu, Shuangqian
AU - Yang, Tong
PY - 2022/3
Y1 - 2022/3
N2 - This paper is concerned with the initial boundary value problem of the Vlasov–Fokker–Planck equation coupled with either the incompressible or compressible Navier–Stokes equations in a bounded domain. The global existence of unique strong solution and its exponential convergence rate to the equilibrium state are proved under the Maxwell boundary condition for the incompressible case and specular reflection boundary condition for the compressible case, respectively. For the compressible model, to overcome the lack of regularity due to the coupling with the kinetic equation in a bounded domain, an essential L10/3 estimate is analyzed so that the a priori estimate can be closed by applying the SPL theory developed by Guo et al. for kinetic models, [Arch Ration Mech Anal 236(3): 1389–1454 (2020)].
AB - This paper is concerned with the initial boundary value problem of the Vlasov–Fokker–Planck equation coupled with either the incompressible or compressible Navier–Stokes equations in a bounded domain. The global existence of unique strong solution and its exponential convergence rate to the equilibrium state are proved under the Maxwell boundary condition for the incompressible case and specular reflection boundary condition for the compressible case, respectively. For the compressible model, to overcome the lack of regularity due to the coupling with the kinetic equation in a bounded domain, an essential L10/3 estimate is analyzed so that the a priori estimate can be closed by applying the SPL theory developed by Guo et al. for kinetic models, [Arch Ration Mech Anal 236(3): 1389–1454 (2020)].
KW - L2-L10/3 estimate
KW - Maxwell boundary condition
KW - Navier–Stokes–Vlasov–Pokker–Plack system
KW - Specular reflection boundary condition
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U2 - 10.1007/s10955-022-02886-7
DO - 10.1007/s10955-022-02886-7
M3 - 21_Publication in refereed journal
VL - 186
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 3
M1 - 42
ER -