Continuous dependence for NLS in fractional order spaces |
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Authors: | Thierry Cazenave Daoyuan Fang |
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Institution: | Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China |
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Abstract: | For the nonlinear Schrödinger equation iut+Δu+λα|u|u=0 in RN, local existence of solutions in Hs is well known in the Hs-subcritical and critical cases 0<α?4/(N−2s), where 0<s<min{N/2,1}. However, even though the solution is constructed by a fixed-point technique, continuous dependence in Hs does not follow from the contraction mapping argument. In this paper, we show that the solution depends continuously on the initial value in the sense that the local flow is continuous Hs→Hs. If, in addition, α?1 then the flow is locally Lipschitz. |
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Keywords: | primary 35Q55 secondary 35B30 46E35 |
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