Well-posedness and small data scattering for the generalized Ostrovsky equation ✩

By Atanas Stefanov, Yannan Shen, Panayotis G. Kevrekidis. 2010

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Abstract We consider the generalized Ostrovsky equation u t x = u + ( u p ) x x . We show that the equation is locally well posed in H s , 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 H 5 ∩ W 3 , 1 and moreover, it scatters small data. The latter results are corroborated by numerical computations which confirm the heuristically expected decay of ‖ u ‖ L r ∼ t − ( r − 2 ) / ( 2 r ) .

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/672b23159c125220e01acac9816d9275047317a7