GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS
GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS
复制标题
DOI：
10.1142/s0218202507002194
复制
发表时间：
2007-07
影响因子：
3.5
通讯作者：
A. Mellet;A. Vasseur
中科院分区：
文献类型：
--
作者：
A. Mellet;A. Vasseur
建立了一类耦合的动力学和流体方程组弱解的存在性。更准确地说，我们考虑一个耦合到可压缩Navier-Stokes方程通过阻力的Vlasov-Fokker-Planck方程。假设流体为正压流体，具有γ-压力定律（γ > 3/2）。在流体速度场满足齐次Dirichlet条件，动力学分布函数满足Dirichlet或反射边界条件的情况下，证明了在λ 3的有界区域内弱解的存在性.
We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov–Fokker–Planck equation coupled to compressible Navier–Stokes equation via a drag force. The fluid is assumed to be barotropic with γ-pressure law (γ > 3/2). The existence of weak solutions is proved in a bounded domain of ℝ3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.