On the low regularity of the Benney-Lin equation |
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| Authors: | Wengu Chen |
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| Affiliation: | a Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China
b College of Mathematics, Beijing Normal University, Beijing 100875, China |
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| Abstract: | We consider the low regularity of the Benney-Lin equation ut+uux+uxxx+β(uxx+uxxxx)+ηuxxxxx=0. We established the global well posedness for the initial value problem of Benney-Lin equation in the Sobolev spaces Hs(R) for 0?s>−2, improving the well-posedness result of Biagioni and Linares [H.A. Biaginoi, F. Linares, On the Benney-Lin and Kawahara equation, J. Math. Anal. Appl. 211 (1997) 131-152]. For s<−2 we also prove some ill-posedness issues. |
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| Keywords: | Benney-Lin equation Initial value problem Well posedness and ill posedness |
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