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Global well-posedness of the Cauchy problem of the fifth-order shallow water equation. (English) Zbl 1106.35068
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 $H^s(\Bbb R)$ provided $s>(5\sqrt{7}-10)/4$.

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