Displaying similar documents to “Blow up and near soliton dynamics for the L 2 critical gKdV equation”

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.

On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴

Changxing Miao, Guixiang Xu, Lifeng Zhao (2010)

Colloquium Mathematicae

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We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H¹(ℝ⁴) data and L²(ℝ⁴) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.

Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems

Pierre Raphaël, Igor Rodnianski (2008-2009)

Séminaire Équations aux dérivées partielles

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This note summarizes the results obtained in []. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the 𝕊 2 target in all homotopy classes and for the equivariant critical S O ( 4 ) Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.

Blow-up of a nonlocal p-Laplacian evolution equation with critical initial energy

Yang Liu, Pengju Lv, Chaojiu Da (2016)

Annales Polonici Mathematici

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This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain. ...

Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension

Frank Merle, Hatem Zaag (2009-2010)

Séminaire Équations aux dérivées partielles

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We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u ( x , t ) , the graph x ↦ T ( x ) of its blow-up points and 𝒮 ⊂ ℝ the set of all characteristic points and show that 𝒮 is locally finite. Finally, given x 0 ∈ 𝒮 , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that...