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- W2271796886 abstract "In this article we treat the Cauchy problem for the dispersive system of long waves, $$ begin{cases} partial_t u + partial_{x}v + upartial_{x}u = 0 partial_t v - partial_{x}^3u + partial_{x}u + partial_{x}(uv) = 0, end{cases} $$ in weighted Sobolev spaces. It is shown that this problem is locally well-posed in $H^s(Bbb R)times H^{s-1}(Bbb R) cap L^2_{gamma}(Bbb R)times H^{-1}_{gamma}(Bbb R)$, for $s>3/2$ and $0leqq gamma leqq s$. The proof involves parabolic regularization and techniques of Bona-Smith. It is also determined, using the orbital stability of the special solitary-wave solutions of this system, that we can extend globally the local solution for data sufficiently close to the solitary wave in the norm $ H^1(Bbb R)times L^{2}(Bbb R)$." @default.
- W2271796886 created "2016-06-24" @default.
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- W2271796886 date "1998-01-01" @default.
- W2271796886 modified "2023-10-15" @default.
- W2271796886 title "A dispersive system of long waves in weighted Sobolev spaces" @default.
- W2271796886 doi "https://doi.org/10.57262/ade/1366399897" @default.
- W2271796886 hasPublicationYear "1998" @default.
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