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 Hs (R), s > −7/4. Moreover, we get global existence for L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and Fourier restriction method are proposed.
Hyder, A., & Zakarya, M. (2019). The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method. Journal of the Egyptian Mathematical Society, 27(1), 1-10. doi: 10.1186/s42787-019-0006-0
MLA
Abd-Allah Hyder; M. Zakarya. "The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method", Journal of the Egyptian Mathematical Society, 27, 1, 2019, 1-10. doi: 10.1186/s42787-019-0006-0
HARVARD
Hyder, A., Zakarya, M. (2019). 'The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method', Journal of the Egyptian Mathematical Society, 27(1), pp. 1-10. doi: 10.1186/s42787-019-0006-0
VANCOUVER
Hyder, A., Zakarya, M. The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method. Journal of the Egyptian Mathematical Society, 2019; 27(1): 1-10. doi: 10.1186/s42787-019-0006-0
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