ar X iv : m at h / 01 04 12 5 v 1 [ m at h . A P ] 1 1 A pr 2 00 1 ON SCHRÖDINGER MAPS
نویسنده
چکیده
We study the question of well-posedness of the Cauchy problem for Schrödinger maps from R×R to the sphere S or to H, the hyperbolic space. The idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear Schrödinger system of equations and then study this modified Schrödinger 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 Schrödinger 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 functions.
منابع مشابه
ar X iv : m at h / 01 04 17 8 v 1 [ m at h . N T ] 1 8 A pr 2 00 1 Arithmetic theory of q - difference equations
Part II. p-adic methods §3. Considerations on the differential case §4. Introduction to p-adic q-difference modules 4.1. p-adic estimates of q-binomials 4.2. The Gauss norm and the invariant χv(M) 4.3. q-analogue of the Dwork-Frobenius theorem §5. p-adic criteria for unipotent reduction 5.1. q-difference modules having unipotent reduction modulo ̟v 5.2. q-difference modules having unipotent redu...
متن کاملar X iv : m at h / 06 04 63 5 v 1 [ m at h . A P ] 2 8 A pr 2 00 6 PARTIAL REGULARITY FOR HARMONIC MAPS , AND RELATED PROBLEMS
Via gauge theory, we give a new proof of partial regularity for harmonic maps in dimensions m ≥ 3 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of ”minimal” C regularity. The proof we present moreover extends to a large class of elliptic systems of quadratic growth.
متن کاملar X iv : h ep - p h / 01 04 19 6 v 2 2 2 A pr 2 00 1 DIFFRACTION AT HERA
A review is presented of diffraction studies at HERA. a a Talk given at the First Workshop on Forward Physics and Luminosity Determination at the LHC, Helsinki, Finland, November 2000.
متن کاملar X iv : m at h / 05 04 37 3 v 1 [ m at h . Q A ] 1 9 A pr 2 00 5 Lax Operator for the Quantised Orthosymplectic
متن کامل
ar X iv : h ep - t h / 01 04 16 1 v 1 1 9 A pr 2 00 1 Gravitating monopoles in SU ( 3 ) gauge theory
We consider the Einstein-Yang-Mills-Higgs equations for an SU(3) gauge group in a spherically symmetric ansatz. Several properties of the gravitating monopole solutions are obtained an compared with their SU(2) counterpart.
متن کامل