GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE*

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doi:10.1007/s10473-023-0102-y

Abstract: In this paper, we consider the weak solutions of compressible Navier-Stokes-Landau-Lifshitz-Maxwell (CNSLLM) system for quantum fluids with a linear density dependent viscosity in a 3D torus. By introducing the cold pressure $P_c$ , we prove the global existence of weak solutions with the pressure $P+P_c$ , where $P = A \rho^{\gamma}$ with $\gamma\ge1$ . Our main result extends the one in [13] on the quantum Navier-Stokes equations to the CNSLLM system.

Key words: compressible Navier-Stokes-Landau-Lifshitz-Maxwell equations, global existence, weak solutions, quantum fluid

Quansen Jiu, Lin Ma. GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*[J].Acta mathematica scientia,Series B, 2023, 43(1): 25-42.

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