The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method
The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method
In this paper, we investigate the Cauchy problem for the stochastic Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in $H^{s}(\mathbb {R})$ , s>−7/4. Moreover, we get global existence for $L^{2}(\mathbb {R})$ solutions. Due to the non-zero singularity of the phase function, …