On universality of blow-up profile for L2 critical nonlinear Schrödinger equation

By F. Merle, Pierre Raphael. 2004

300 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/51e43f7afc66b97cf29af8fb8b8237d1488cec5a

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (2011, background): “However, in [47], for the NLS equation, the result goes further and clarifies the blow-up for super-critical masses close to critical.”
Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation (2008, methodology): “Remark: The techniques are based on a very good understanding of the behavior of the solution in selfsimilar variables in the energy space related to the selfsimilar variable, together with a Liouville Theorem (see Theorem 2). For a similar approach of the blow-up problem, see Martel and Merle [11],”
On collapsing ring blow up solutions to the mass supercritical NLS (2012, background): “The situation is better understood in the mass critical case sc = 0 since the series of works [33], [23], [24], [25], [26], [27] where a stable blow up regime of "log-log" type is exhibited in dimension N ≤ 5 with a complete description of the associated bubble of concentration.”
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension (2007, methodology): “This difficulty will be overcome by using similar concepts to those used for the Korteweg de Vries equation (Martel and Merle [13]) and the nonlinear Schrödinger equation (Merle and Raphaël [14]).”
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].”
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation (2005, methodology): “This question was first investigated in [ 13 ] but in the rescaled variable, which corresponds to the proof of asymptotic stability of the soliton in the blow up regime (11).”
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation (2009, background): “by Merle and Rapha¨el, by classification of solutions that are nondispersive (in a weak sense) [ MR04 ].”
Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation (2006, methodology): “It was also remarked in [14,16] that the linear operators L1, L2 given by (6) are related through a remarkable commutation formula to the standard linear operators close to the ground state, as studied by Weinstein in [26] and given by”
Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain (2007, background): “Such a radiation is the non L2 tail of the self similar solutions to (24), see Lemma 15 in [21].”