Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation

الأصل · EN

We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation u_t-D_xαu_x + u_xyy = uu_x, (t,x,y)∈³, 1≤ α≤ 2,is locally well-posed in the spaces Eˢ, s 2α- 34, endowed with the normf_Eˢ = |ξ|α+μ²ˢf_L²(²).As a consequence, we get the global well-posedness in the energy space E¹/² as soon as α 85. The proof is based on the approach of the short time Bourgain spaces developed by Ionescu, Kenig and Tataru IKT combined with new Strichartz estimates and a modified energy.