Global solutions to the bipolar non-isentropic Euler-Maxwell system in the Besov framework

This paper investigates the bipolar non-isentropic compressible Euler-Maxwell system in $ \mathbb {R}<^>{3} $ R3 and $ \mathbb {T}<^>{3} $ T3. For both problems, we establish the global existence of smooth solutions in the general Besov spaces, which covers the usual Sobolev spaces with higher regularity and the critical Besov space, when the initial perturbations around the constant states are small enough. As a byproduct, we obtain the large-time asymptotic behavior of the global solutions near the equilibrium state in the general Besov spaces with relatively lower regularity. The proof is based on the technical Fourier frequency-localization method developed through the Littlewood-Paley theory, but some new development and technique are proposed for treating the strong coupling and nonlinearity for the bipolar non-isentropic case.