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Zbl 0808.35142
Tsutsumi, M.
Decay of weak solutions to the Davey-Stewartson systems. (English)
[J] J. Math. Anal. Appl. 182, No.3, 680-704 (1994). ISSN 0022-247X

One considers the initial value problem for the Davey-Stewartson system of elliptic-hyperbolic type which appears quite naturally as the envelope equations in the study of water waves. The aim of the paper is to establish the global existence of weak solutions which satisfy a structural inequality referred to as pseudo-conformal inequality, and to obtain decay estimates of these weak solutions.\par The first introductory section states the main result, section 2 proposes a suitable approximate equation which regularizes the DS system and constructs strong solutions to the regularized problem. Section 3 provides a priori estimates, and the last section displays the proof of the main theorem.
[G.Jumarie (Montreal)]

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35D05 Existence of generalized solutions of PDE
35B40 Asymptotic behavior of solutions of PDE

Keywords: pseudo-conformal inequality; decay estimates; a priori estimates

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