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Article Dans Une Revue Advances in Differential Equations Année : 2004

SCHRODINGER GROUP ON ZHIDKOV SPACES

Résumé

We consider the Cauchy problem for nonlinear Schrödinger equations on R n with nonzero boundary condition at infinity, a situation which occurs in stability studies of dark solitons. We prove that the Schrödinger operator generates a group on Zhidkov spaces X k (R n) for k > n/2, and that the Cauchy problem for NLS is locally well-posed on the same Zhidkov spaces. We justify the conservation of classical invariants which implies in some cases the global well-posedness of the Cauchy problem.
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Dates et versions

hal-01960986 , version 1 (08-01-2019)

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  • HAL Id : hal-01960986 , version 1

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Clément Gallo. SCHRODINGER GROUP ON ZHIDKOV SPACES. Advances in Differential Equations, 2004, 9, pp.509 - 538. ⟨hal-01960986⟩
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