Asymptotic decay of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell systems

Abstract The initial value problems of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell (CNS-M) systems arising from plasmas in R 3 are studied. The main difficulty of studying the bipolar isentropic/non-isentropic CNS-M systems lies in the appearance of the electromagnetic fields satisfying the hyperbolic Maxwell equations. The large time-decay rates of global smooth solutions with small amplitude in L q ( R 3 ) for 2 ≤ q ≤ ∞ are established. For the bipolar non-isentropic CNS-M system, the difference of velocities of two charged carriers decay at the rate ( 1 + t ) − 3 4 + 1 4 q which is faster than the rate ( 1 + t ) − 3 4 + 1 4 q ( ln ⁡ ( 3 + t ) ) 1 − 2 q of the bipolar isentropic CNS-M system, meanwhile, the magnetic field decay at the rate ( 1 + t ) − 3 4 + 3 4 q ( ln ⁡ ( 3 + t ) ) 1 − 2 q which is slower than the rate ( 1 + t ) − 3 4 + 3 4 q for the bipolar isentropic CNS-M system. The approach adopted is the classical energy method but with some new developments, where the techniques of choosing symmetrizers and the spectrum analysis on the linearized homogeneous system play the crucial roles.