Abstract
This paper is devoted to investigating the convergence problem of the nonlinear Schrödinger equation and the nonlinear wave equation. Firstly, the almost everywhere pointwise convergence of the one-dimensional nonlinear Schrödinger equation is established in Hs(R)(s≥14) with the aid of the decomposition of integral form solution to problem. Secondly, the uniform convergencelimt→0supx∈R|u(x,t)−S1(t)f|=0 is established with initial data in Hs(R)(s>0), where u is the solution to the one-dimensional nonlinear Schrödinger equation and S1(t)f is the solution to the free one-dimensional Schrödinger equation. Finally, the almost everywhere pointwise convergence of the nonlinear wave equation is established in Hs(R3)(s>1).
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