The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method
Hyder, A., Zakarya, M. (2019). The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method. EKB Journal Management System, 27(1), 1-10. doi: 10.1186/s42787-019-0006-0
Abd-Allah Hyder; M. Zakarya. "The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method". EKB Journal Management System, 27, 1, 2019, 1-10. doi: 10.1186/s42787-019-0006-0
Hyder, A., Zakarya, M. (2019). 'The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method', EKB Journal Management System, 27(1), pp. 1-10. doi: 10.1186/s42787-019-0006-0
Hyder, A., Zakarya, M. The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method. EKB Journal Management System, 2019; 27(1): 1-10. doi: 10.1186/s42787-019-0006-0

The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method

Journal of the Egyptian Mathematical Society
Article 5, Volume 27, Issue 1, 2019, Pages 1-10    PDF (588.23 K)
DOI: 10.1186/s42787-019-0006-0
Authors
Abd-Allah Hyder; M. Zakarya
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004 Abha, Saudi Arabia
Abstract
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.

Keywords
Kawahara equation; Well-posedness; Wiener process; Fixed point theorem; Fourier restriction method
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