Persistence of Solutions to Nonlinear Evolution Equations in Weighted Sobolev Spaces
نویسندگان
چکیده
In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces X s,θ, for s ≥ 2θ ≥ 2 and the initial value problem associated with the nonlinear Schrödinger equation is well-posed in weighted Sobolev spaces X s,θ, for s ≥ θ ≥ 1. Persistence property has been proved by approximation of the solutions and using a priori estimates.
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