GLOBAL WEAK SOLUTIONS TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL*

doi:10.1007/s10473-023-0510-z

Abstract

Abstract: In this paper, we study a quantum kinetic-fluid model in a three-dimensional torus. This model is a coupling of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate viscosity. We establish a global weak solution to this model for arbitrarily large initial data when the pressure takes the form $ p(\rho)=\rho^\gamma+p_c(\rho)$, where $\gamma>1$ is the adiabatic coefficient and $p_c(\rho)$ satisfies \begin{equation*} p_c(\rho)=\left\{ \begin{array}{ll}-c\rho^{-4k}\; \;\;\;&{\rm{if}}\;\;\rho\leq 1, \\ \rho^{\gamma}\;\;\;\;&{\rm{if}}\;\;\rho>1 \end{array} \right. \end{equation*} for $k\geq 4$ and some constant $c>0$.

Key words: kinetic-fluid model, quantum Bohm potential, density-dependent viscosity, weak solutions

CLC Number:

35Q35

Fucai Li, Yue Li, Baoyan Sun. GLOBAL WEAK SOLUTIONS TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL^*[J].Acta mathematica scientia,Series B, 2023, 43(5): 2089-2107.

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GLOBAL WEAK SOLUTIONS TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL^*

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