Local well-posedness result for a class of non-local quasi-linear systems and its application to the justification of Whitham-Boussinesq systems

2022/06/18 by Emerald, Louis · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2206.09213

Abstract

In this paper we prove a local well-posedness result for a class of quasi-linear systems of hyperbolic type involving Fourier multipliers. Among the physically relevant systems in this class is a family of Whitham-Boussinesq systems arising in the modeling free-surface water waves. Our result allows to prove the rigorous justification of these systems as approximations to the general water waves system on a relevant time scale, independent of the shallowness parameter.

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• The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems

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