000155192 001__ 155192
000155192 005__ 20180913060120.0
000155192 0247_ $$2doi$$a10.1016/j.aim.2009.02.017
000155192 037__ $$aARTICLE
000155192 245__ $$aRenormalization and blow up for the critical Yang-Mills problem
000155192 269__ $$a2009
000155192 260__ $$c2009
000155192 336__ $$aJournal Articles
000155192 520__ $$aWe consider the Yangs-Mills equations in 4 + 1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are obtained by the spherically symmetric ansatz in the SO(4) gauge group and result by rescaling of the instanton solution. The rescaling is done via a prescribed rate which in this case is a modification of the self-similar rate by a power of vertical bar log t vertical bar. The powers themselves take any value exceeding 3/2 and thus form a continuum of distinct rates leading to blow-up. The methods are related to the authors' previous work on wave maps and the energy critical semi-linear equation. However, in contrast to these equations, the linearized Yang-Mills operator (around an instanton) exhibits a zero energy eigenvalue rather than a resonance. This turns out to have far-reaching consequences, amongst which are a completely different family of rates leading to blow-up (logarithmic rather than polynomial corrections to the self-similar rate). (C) 2009 Elsevier Inc. All rights reserved.
000155192 6531_ $$aNonlinear wave equations
000155192 6531_ $$aBlow up
000155192 6531_ $$aCritical phenomena
000155192 6531_ $$a4-Dimensional Minkowski Space
000155192 6531_ $$aGlobal Existence
000155192 6531_ $$aWave Maps
000155192 6531_ $$aHiggs Fields
000155192 6531_ $$aEquations
000155192 6531_ $$aDimensions
000155192 700__ $$0244702$$aKrieger, Joachim$$g199126
000155192 700__ $$aSchlag, W.
000155192 700__ $$aTataru, D.
000155192 773__ $$j221$$q1445-1521$$tAdvances In Mathematics
000155192 8564_ $$s491297$$uhttps://infoscience.epfl.ch/record/155192/files/ymj0911.pdf$$yn/a$$zn/a
000155192 909C0 $$0252322$$pPDE$$xU12235
000155192 909CO $$ooai:infoscience.tind.io:155192$$pSB$$particle
000155192 917Z8 $$x139598
000155192 937__ $$aEPFL-ARTICLE-155192
000155192 973__ $$aOTHER$$rREVIEWED$$sPUBLISHED
000155192 980__ $$aARTICLE