Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation

By F. Merle, Pierre Raphael. 2005

215 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/da320489206cb8a59df1175bfb362c8f047e41f9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

Citations in the corpus

Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain (2007, background): “Note that the argument in [23] relies again only on L2 uxes computations which do not involve boundary terms as we saw for the proof of Lemma 8 , and thus the analysis applies.”
The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities (2005, background): “For results on this problem and a more detailed list of references see [17, 18].”
Classification of radial solutions of the focusing, energy-critical wave equation (2012, methodology): “Results of this type for other equations in the global case include those for data close to the soliton for subcritical nonlinearities: see the works of Martel and Merle [27] in the case of generalized KdV equations, of Buslaev and Perelman [4, 3] in the case of one dimensional NLS with specific non”
On collapsing ring blow up solutions to the mass supercritical NLS (2012, background): “This is a spectacular difference with the mass critical problem sc = 0 where the amount of mass focused by the nonlinearity is conjectured to be quantized, see [27].”
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation (2009, unknown): “A similar phenomenon is highlighted in the context of the nonlinear Schr¨odinger equation in [ MR05 , MR08].”
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].”
Nonradial type II blow up for the energy-supercritical semilinear heat equation (2016, background): “In the energy critical case p = d+2 d−2 , d = 4, Schweyer constructed in [45] a radial type II blow-up solution, following the analysis of critical problems [30, 28, 29, 43, 44, 42, 31].”
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation (2010, unknown): “106 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110”
Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation (2006, unknown): “Theorem 1 (Dynamics of (1), [14–18,22]).”
Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems (2009, background): “For the latter problem the sharp blow up speed and the quantization of the blow up mass is derived in [25], [26], [27].”