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Displaying similar documents to “A pseudoconformal compactification of the nonlinear Schrödinger equation and applications.”

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 H ^ s r ℝ defined by the norm v 0 H ^ s r ℝ : = ξ s v 0 ^ L ξ r ' , ξ = 1 + ξ 2 1 2 , 1 r + 1 r ' = 1 . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ 2 j - 1 2 r ' . 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 < 2 j - 1 2 r ' . The results for r =...

Remarks on global existence and compactness for L 2 solutions in the critical nonlinear schrödinger equation in 2D

Luis Vega Gonzalez (1998)

Journées équations aux dérivées partielles

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In the talk we shall present some recent results obtained with F. Merle about compactness of blow up solutions of the critical nonlinear Schrödinger equation for initial data in L 2 ( 𝐑 2 ) . They are based on and are complementary to some previous work of J. Bourgain about the concentration of the solution when it approaches to the blow up time.