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Wang, Hua; Cui, Shangbin

Global well-posedness of the Cauchy problem of the fifth-order shallow water equation. (English) Zbl 1106.35068

J. Differ. Equations 230, No. 2, 600-613 (2006).
Summary: By using the \(I\)-method, we prove that the Cauchy problem of the fifth-order shallow water equation \[ \partial_tu- \partial_x^2 \partial_tu+ \partial_x^3u+ 3u\partial_xu- 2\partial_xu \partial_x^2u- u\partial_x^3u- \partial_x^5u=0 \] is globally well-posed in the Sobolev space \(H^s(\mathbb R)\) provided \(s>(5\sqrt{7}-10)/4\).

Cited in 12 Documents

MSC:

35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
35G25 Initial value problems for nonlinear higher-order PDEs

Keywords:

fifth-order shallow water equation; global well-posedness; \(I\)-method
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\textit{H. Wang} and \textit{S. Cui}, J. Differ. Equations 230, No. 2, 600--613 (2006; Zbl 1106.35068)
Full Text: DOI

References:

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