Well-posedness of stochastic modified Kawahara equation

Résumé

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 $H^{s}(\mathbb{R})$ Hs(R) , $s\geq -1/4$ s≥−1/4 . Moreover, we get the global existence for $L^{2}( \mathbb{R})$ 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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