Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation

By F. Merle, Pierre Raphael. 2003

259 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fd07545bcd0b375b5927fb655a50750403b54fb9

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Why are solitons stable (2008, unknown): “For instance, see [60], [61], [62] for some results relating to the mass-critical NLS.”
Determination of the blow-up rate for a critical semilinear wave equation (2005, background): “The wave equation has no new blow-up rate at the critical case, unlike NLS where new blow-up rates appear at the critical case (with respect to the conformal invariance), see Merle and Raphaël [13], [12], [14], or the semilinear heat equation where we have new blow-up rates at the critical case (wit”
Minimal-mass blowup solutions of the mass-critical NLS (2006, unknown): “[2], [4], [6], [7], [8], [17], [20], [21], [22], [23], [24], [25], [26], [27], [39].”
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation (2005, background): “Theorem 1 ([6],[ 7 ]) There exists > 0 and C such that the following is true.”
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation (2005, methodology): “We recall from [ 12 ] the existence of a one parameter family of localized self similar profiles in the vicinity of ground state solution Q. Let a parameter 0 12 ].”
Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton (2014, methodology): “We omit the details and refer for example to [27] for a proof with similar Qb profiles for the NLS case.”
Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain (2007, methodology): “The proof of Lemma 3 is similar to the one of Lemma 2 in [20] up to minor modi cations which we now detail.”
The cubic nonlinear Schr\"odinger equation in two dimensions with radial data (2007, background): “In a series of papers [41, 42, 43], Merle and Raphael gave a more or less complete description of blowup behaviour at masses slightly above that of the ground state (and finite energy).”
Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS (2010, background): “This construction generalizes the one introduced in [27], see also [15] for”
Blow up for the critical gKdV equation II: minimal mass dynamics (2012, methodology): “In Part I [33], we have revisited the blow up analysis in light of recent developments related to blow up for the mass critical Schrödinger equation [39, 40, 41, 42, 43, 44] and energy critical geometrical equations [50, 45, 51].”
On universality of blow-up profile for L2 critical nonlinear Schrödinger equation (2004, methodology): “Results in this paper together with sharp upper bound on blow up speed of paper [ 23 ] answer this type of questions in the L 2 vicinity of Q.”