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Global existence for small data of the viscous Green-Naghdi type equations. (English) Zbl 1358.35123

This paper is concerned with the global existence of smooth solutions to the Cauchy problem for the Green-Naghdi equations with viscosity and small initial data; it is deduced that the constant solutions are asymptotically stable.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
35L10 Second-order hyperbolic equations
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