A note on the 2D generalized Zakharov-Kuznetsov equation: Local, global, and scattering results

作者：Farah Luiz G; Linares Felipe^*; Pastor Ademir

来源：Journal of Differential Equations, 2012, 253(8): 2558-2571.

DOI：10.1016/j.jde.2012.05.019

• Local and global well-posedness
• Nonlinear scattering

We consider the generalized two-dimensional Zakharov-Kuznetsov equation u(t) + partial derivative(x)Delta u + partial derivative(x)(u(k+1)) = 0, where k %26gt;= 3 is an integer number. For k %26gt;= 8 we prove local well-posedness in the L-2-based Sobolev spaces H-s(R-2), where s is greater than the critical scaling index s(k) = 1 - 2/k. For k %26gt;= 3 we also establish a sharp criteria to obtain global H-1(R-2) solutions. A nonlinear scattering result in H-1(R-2) is also established assuming the initial data is small and belongs to a suitable Lebesgue space.

• 出版日期2012-10-15