Two singular dynamics of the nonlinear Schrödinger equation on a plane domain

By Nicolas Burq, P. Gérard, N. Tzetkov. 2003

62 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7b710051abb1274e2182ff71734f9fe2d5757201

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In Control and Systems Engineering

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Random data Cauchy theory for supercritical wave equations I: local theory (2007, methodology): “In fact, recently, several methods to show ill-posedness, or high frequency instability, for s scr emerged (see the works by Burq, Gérard and Tzvetkov [6, 5], Lebeau [12] and Christ Colliander and Tao [10]).”
Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain (2007, methodology): “On the sharpness of lower bound (19): The critical mass blow-up solutions build in [5] satisfy |∇u(t)|L2 ∼ C(u0) T − t .”
Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS (2010, background): “In the presence of a very smooth and flat k at x0, the existence of critical elements may be derived using a brutal fixed point argument, [25], [24], [6], see also [14] for related statements in the setting of nonlocal nonlinearities.”
Nonlinear wave interactions for the Benjamin-Ono equation. (2004, background): “Moreover, essentially all papers [6, 7, 8, 12] deal with the self interaction of a single high frequency wave which naturally lead to upper bounds on the Sobolev regularity s which is consistent with the smooth dependence on the initial data for large s holding in the cases considered in [6, 7, 8, 1”
Blow up for the critical gKdV equation II: minimal mass dynamics (2012, background): “6) – in contrast with direct perturbative methods developed in [3], [4], [1], see also [20] for existence in the one dimensional half wave problem.”