Universality of Blow up Profile for Small Blow up Solutions to the Energy Critical Wave Map Equation
نویسندگان
چکیده
منابع مشابه
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation
Consider the energy critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, u...
متن کاملSmooth type II blow up solutions to the four dimensional energy critical wave equation
We exhibit C∞ type II blow up solutions to the focusing energy critical wave equation in dimension N = 4. These solutions admit near blow up time a decomposiiton u(t, x) = 1 λ N−2 2 (t) (Q+ ε(t))( x λ(t) ) with ‖ε(t), ∂tε(t)‖Ḣ1×L2 ≪ 1 where Q is the extremizing profile of the Sobolev embedding Ḣ → L∗ , and a blow up speed λ(t) = (T − t)e− √ |log(T−t)|(1+o(1)) as t → T.
متن کاملSlow Blow up Solutions for Certain Critical Wave Equations
We describe in this article two recent results [11], [12], obtained by the author jointly with W. Schlag and D. Tataru, about singular solutions for the critical wave maps equation, as well as the critical focussing semilinear wave equation. Specifically, the first result [11] establishes for the first time the conjectured formation of singularities for co-rotational wave maps into the sphere S...
متن کاملStability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
The generalized Korteweg-de Vries equations are a class of Hamiltonian systems in infinite dimension derived from the KdV equation where the quadratic term is replaced by a higher order power term. These equations have two conservation laws in the energy space H1 (L2 norm and energy). We consider in this paper the critical generalized KdV equation, which corresponds to the smallest power of the...
متن کاملBlow up Dynamic and Upper Bound on the Blow up Rate for critical nonlinear Schrödinger Equation
We consider the critical nonlinear Schrödinger equation iut = −∆u − |u| 4 N u with initial condition u(0, x) = u0 in dimension N . For u0 ∈ H1, local existence in time of solutions on an interval [0, T ) is known, and there exists finite time blow up solutions, that is u0 such that limt→T<+∞ |ux(t)|L2 = +∞. This is the smallest power in the nonlinearity for which blow up occurs, and is critical...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2017
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnx073