Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation

1998/05/01 by Adrian Constantin, Joachim Escher · 34 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Navier-Stokes equation solutions

paper · doi:10.1002/(sici)1097-0312(199805)51:5<475::aid-cpa2>3.0.co;2-5

Abstract

We establish the local well-posedness of a recently derived model for small-amplitude, shallow water waves. For a large class of initial data we prove global existence of the corresponding solution. Criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained, and an existence and uniqueness result for a class of global weak solutions is also given. © 1998 John Wiley & Sons, Inc.

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