Global well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations

TL;DR

This paper establishes the local and global well-posedness, blow-up criteria, and long-term behavior of solutions to the two-fluid Euler-Maxwell equations in critical Besov spaces, highlighting differences from the one-fluid case.

Contribution

It provides the first analysis of well-posedness and asymptotic behavior for two-fluid Euler-Maxwell equations in critical Besov spaces, addressing nonlinear coupling complexities.

Findings

Local existence and blow-up criteria established

Global solutions exist for small initial data

Large-time asymptotic behavior characterized

Abstract

In this paper, we study the well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations, which is different from the one fluid case. We need to deal with the difficulties mainly caused by the nonlinear coupling and cancelation between two carriers. Precisely, we first obtain the local existence and blow-up criterion of classical solutions to the Cauchy problem and periodic problem pertaining to data in Besov spaces with critical regularity. Furthermore, we construct the global existence of classical solutions with aid of a different energy estimate (in comparison with the one-fluid case) provided the initial data is small under certain norms. Finally, we establish the large-time asymptotic behavior of global solutions near equilibrium in Besov spaces with relatively lower regularity.