Boa colocação do problema de Cauchy para a equação de Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK)

Abstract

In this dissertation we study the initial value problem associated with the Benjamin-Ono- Zakharov-Kuznetsov equation. We prove the local well-posedness of the IVP in the usual Sobolev spaces Hs (R2), s > 2, and in the anisotropic spaces Hs1,s2 (R2), s2 > 2, s1 ≥ s2. We also investigate the persistence properties of the solution and the local well-posedness in weighted Sobolev spaces Zs,r = Hs (R2)∩L2((1 + x 2 + y2)r dxdy), where s > 2, r ≥ 0, and s ≥ 2r . Unique continuation principles are also proved, showing that our persistence properties are sharp.