Local well-posedness of quasi-linear systems generalizing KdV
نویسندگان
چکیده
منابع مشابه
Global Well-posedness of Nls-kdv Systems for Periodic Functions
We prove that the Cauchy problem of the Schrödinger-KortewegdeVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1×H1. More precisely, we show that the nonresonant NLS-KdV system is globally well-posed for initial data in Hs(T) × Hs(T) with s > 11/13 and the resonant NLS-KdV system is globally wellposed with s > 8/9. The strategy is to app...
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We consider the local well-posedness problem of a one-parameter family of coupled KdV-type systems both in the periodic and non-periodic setting. In particular, we show that certain resonances occur, closely depending on the value of a coupling parameter α when α 6= 1. In the periodic setting, we use the Diophantine conditions to characterize the resonances, and establish sharp local well-posed...
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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 study the Cauchy problem for the modified KdV equation ut + uxxx + (u )x = 0, u(0) = u0 for data u0 in the space Ĥr s defined by the norm ‖u0‖Ĥr s := ‖〈ξ〉 sû0‖Lr′ ξ . Local well-posedness of this problem is established in the parameter range 2 ≥ r > 1, s ≥ 1 2 − 1 2r , so the case (s, r) = (0, 1), which is critical in view of scaling considerations, is almost reached. To show this result, we...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2012
ISSN: 1534-0392
DOI: 10.3934/cpaa.2013.12.899