On sharp global well-posedness and ill-posedness for a fifth-order KdV-BBM type equation
نویسندگان
چکیده
منابع مشابه
Sharp Global Well - Posedness for Kdv and Modified Kdv On
The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all L 2-based Sobolev spaces H s where local well-posedness is presently known, apart from the H 1 4 (R) endpoint for mKdV. The result for KdV relies on a new method for co...
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We prove that the KdV-Burgers is globally well-posed in H−1(T) with a solution-map that is analytic fromH−1(T) to C([0, T ];H−1(T)) whereas it is ill-posed in Hs(T), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(T) to even D′(T) at any fixed t > 0 small enough. In view of the result of Kappeler and Topalov for KdV it thus appears that even if the dis...
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We complete the known results on the Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in H−1(R) with a solution-map that is analytic from H−1(R) to C([0, T ];H−1(R)) whereas it is ill-posed in Hs(R), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(R) to even D′(R) at any fixed t > 0 small enough....
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The regularized long-wave or BBM equation ut + ux + uux − uxxt = 0 was derived as a model for the unidirectional propagation of long-crested, surface water waves. It arises in other contexts as well, and is generally understood as an alternative to the Korteweg-de Vries equation. Considered here is the initial-value problem wherein u is specified everywhere at a given time t = 0, say, and inqui...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2019
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2019.06.045