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Well-posedness of the Cauchy problem of Ostrovsky equation in analytic Gevrey spaces and time regularity. (English) Zbl 1462.35139

Summary: We study the Cauchy problem of the Ostrovsky equation (Ost) \(\partial_tu+\partial_x^3u-\partial_x^{-1}u+u\partial_xu=0\), where the data in analytic Gevrey spaces on the line and the circle is considered and its local well-posedness in these spaces is proved. The proof is based on bilinear estimates in Bourgain type spaces. Also, Gevrey regularity of the solution in time variable is provided.

MSC:

35G15 Boundary value problems for linear higher-order PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35B65 Smoothness and regularity of solutions to PDEs
35C07 Traveling wave solutions
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