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Título : A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
Autor : Álvarez Samaniego, Borys Yamil
Lannes, David
Palabras clave : ONDAS DE AGUA
SERRE Y GREENNAGHDI
Fecha de publicación : ene-2007
Editorial : Francia: Archive ouverte HAL
Citación : Álvarez Samaniego, Borys y Lannes, David (2007). A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations. Indiana University Mathematics Journal, 1-26
Resumen : Abstract. We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and GreenNaghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations.
URI : http://www.dspace.uce.edu.ec/handle/25000/14457
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