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) Hs(R) , s≥ -1/4 s≥−1/4 . Moreover, we get the global existence for L²( R) L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.
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Agarwal et al. (2020) studied this question.