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On the Benney-Lin and Kawahara equations. (English) Zbl 0876.35100

Summary: We establish global well-posedness for the initial value problem (IVP) associated to the so-called Benney-Lin equation \[ u_t+ uu_x+ u_{xxx}+ \beta(u_{xx}+ u_{xxxx})+ \eta u_{xxxxx}=0,\;u(x,0)=\phi(x). \] This model is a Korteweg-de Vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics. We also study the limiting behaviour of solutions to this IVP when the parameters of the perturbed terms approach \(0\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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References:

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