Displaying similar documents to “Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov–Poisson system”

Blow up and near soliton dynamics for the L 2 critical gKdV equation

Yvan Martel, Frank Merle, Pierre Raphaël (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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These notes present the main results of [, , ] concerning the mass critical (gKdV) equation u t + ( u x x + u 5 ) x = 0 for initial data in H 1 close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in H 1 , construction of various exotic blow up rates in H 1 , including grow up in infinite time. ...

Two blow-up regimes for L 2 supercritical nonlinear Schrödinger equations

Frank Merle, Pierre Raphaël, Jérémie Szeftel (2009-2010)

Séminaire Équations aux dérivées partielles

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We consider the focusing nonlinear Schrödinger equations i ∂ t u + Δ u + u | u | p - 1 = 0 . We prove the existence of two finite time blow up dynamics in the supercritical case and provide for each a qualitative description of the singularity formation near the blow up time.

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.