Well-posedness and small data scattering for the generalized Ostrovsky equation |
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| Authors: | Atanas Stefanov P.G. Kevrekidis |
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| Affiliation: | a Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS 66045-7523, United States
b Lederle Graduate Research Tower, Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, United States |
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| Abstract: | We consider the generalized Ostrovsky equation utx=u+(up)xx. We show that the equation is locally well posed in Hs, s>3/2 for all integer values of p?2. For p?4, we show that the equation is globally well posed for small data in H5∩W3,1 and moreover, it scatters small data. The latter results are corroborated by numerical computations which confirm the heuristically expected decay of ‖uLr‖∼t−(r−2)/(2r). |
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