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On Schrodinger maps
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DOI：10.1002/cpa.10054.png)
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Abstract
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We study the question of well-posedness of the Cauchy problem for Schrodinger maps from R-1 x R-2 to the sphere S-2 or to H-2, the hyperbolic space. The idea is to choose an appropriate gauge.change so that the derivatives of the map will satisfy a certain nonlinear Schrodinger system of equations and then study this modified Schrodinger map system (MSM). We then prove local well-posedness of the Cauchy problem for the MSM with minimal regularity assumptions on the data and outline a method to derive well-posedness of the Schrodinger map itself from it. In proving well-posedness of the MSM, the heart of the matter is resolved by considering truly quatrilinear forms of weighted L-2-functions. (C) 2002 Wiley Periodicals, Inc.
Keywords:
INITIAL-VALUE PROBLEM
WAVE MAPS
CAUCHY-PROBLEM
NULL FORMS
EQUATIONS
REGULARITY
EXISTENCE
SYSTEM
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