Global well-posedness of classical solution to the interactions between short-long waves with large initial data

Abstract

We present the global existence and uniqueness of the classical solution to a system describing the interactions of short waves and long waves. This coupled system is formed by the compressible micropolar equations in Eulerian coordinates and the Schrödinger equation in Lagrangian coordinates. This paper establishes a sufficient frame condition to guarantee the well-posedness of the coupled system with large initial data in the two-dimensional torus.