Well-posedness of Non-Linear Partial Differential Equations in Weighted Sobolev Spaces

The well-posedness (existence, uniqueness, and stability) of the solutions for several nonlinear dispersive PDEs with initial data in Sobolev spaces has been intensively analyzed. However, Sobolev functions do not necessarily decay fast at infinity, which is in many applications an unrealistic assumption. In this talk, we discuss examples of existence and uniqueness results in weighted Sobolev spaces, for the derivative nonlinear Schrodinger equation and the nonlinear Schrodinger-Airy equation.

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