The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in weighted Sobolev spaces

2013/05/02 by Alysson Cunha, Cunha, Alysson, Ademir Pastor +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1305.0509

arxiv created 2013/05/02 · arxiv updated 2013/05/03

Abstract

In this paper we study the initial-value problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation. We prove that the IVP for such equation is locally well-posed in the usual Sobolev spaces H^s(\R²), s>2, and in the anisotropic spaces H^s₁,s₂(\R²), s₂>2, s₁≥ s₂. We also study the persistence properties of the solution and local well-posedness in the weighted Sobolev class Z_s,r=H^s(\R²)∩ L²((1+x² +y²)^rdxdy), where s>2, r≥ 0, and s≥ 2r. Unique continuation properties of the solution are also established. These continuation principles show that our persistence properties are sharp. Most of our arguments are accomplished taking into account that ones for the Benjamin-Ono equation.

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