一类二维广义Zakharov方程的适定性

Well-posedness for a Two-dimensional Generalized Zakharov Equations

摘要: 考虑一类广义Zakharov方程的Cauchy问题的适定性. 通过一系列的先验估计, 利用Galerkin方法, 对于二维广义Zakharov方程的Cauchy问题得到了整体光滑解的存在性和惟一性.

Abstract: The existence and uniqueness of solutions to the Cauchy problem for a class of generalized Zakharov equations in two-dimensions are investigated. By virtue of a priori integral estimate and Galerkin method, the global existence and uniqueness of the solution to the problem are established.