Global existence and the time decay estimates of solutions to the compressible quantum Navier–Stokes–Maxwell system in R3$\mathbb {R}^3$

Abstract

AbstractWe consider the Cauchy problem of the compressible quantum Navier–Stokes–Maxwell equations with the linear damping in the isentropic case under the small perturbation of the constant equilibrium state in three dimensions. Based on the refined energy method, we establish the classical solution globally in time in Sobolev space. By the combination of the energy estimates with the interpolation between the positive Sobolev norms and the negative Sobolev norms with , we also obtain the algebraic decay rates of the classical solution. What is more, the –L2 types of the time decay rates of the solution are obtained without small assumption on the initial data in L1 norm.