On the Cauchy problem for the generalized shallow water wave equation |
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| Authors: | Lixin Tian Guilong Gui |
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| Institution: | a Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China
b Department of Mathematics, University of Texas, Arlington, TX 76019, USA |
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| Abstract: | In this paper we mainly study the Cauchy problem for the generalized shallow water wave equation in the Sobolev space Hs of lower order s. Using the crucial bilinear estimates in the Fourier transform restriction spaces related to the shallow water wave equation, we establish local well-posedness in Hs with any  . |
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| Keywords: | 35Q53 35A07 |
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