Random data Cauchy problem for supercritical Schrödinger equations
Laurent Thomann (2009)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “A smoothing property for the -critical NLS equations and an application to blowup theory”
Random data Cauchy problem for supercritical Schrödinger equations
On nonlinear Schrödinger equations in exterior domains
N Burq, P Gérard, N Tzvetkov (2004)
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The Cauchy problem for the Gross–Pitaevskii equation
P. Gérard (2006)
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On the Dirac delta as initial condition for nonlinear Schrödinger equations
V. Banica, L. Vega (2008)
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Global existence of small classical solutions to nonlinear Schrödinger equations
Tohru Ozawa, Jian Zhai (2008)
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On the hierarchies of higher order mKdV and KdV equations
Axel Grünrock (2010)
Open Mathematics
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The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces defined by the norm . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ . The proof uses an appropriate variant of the Fourier restriction norm method. A counterexample is discussed to show that the Cauchy problem for equations of this type is in general ill-posed in the C 0-uniform sense, if s < . The results for r =...