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Local Well-Posedness of the Nonlinear Schrödinger and the Korteweg-de Vries Equations on the Line
Lee, Jaekang
Lee, Jaekang
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Abstract
The Hadamard local well-posedness of the initial value problem on the infinite line for the nonlinear Schrödinger and the Korteweg-de Vries equations is established for initial data in Sobolev spaces. The proofs presented are due to the seminal works by Tsutsumi and Kenig, Ponce and Vega, respectively, and rely on a contraction mapping argument combined with delicate linear estimates that are shown via the use of harmonic analysis techniques. The different tools used for each of the two equations are due to the different nature of their nonlinearities, which leads to the different types of function spaces for their solutions.
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2023-05-01
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University of Kansas
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987754_1.pdf
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Keywords
Mathematics, dispersive pdes, kdv, korteweg-de vries, nls, nonlinear schrödinger, well-posedness