Well-posedness of stochastic modified Kawahara equation

Abstract

In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in Hs(R) , s≥ − 1 / 4. Moreover, we get the global existence for L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.