Full range of blow up exponents for the quintic wave equation in three dimensions

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• 作者：Joachim Kriegerup>aup>up> ; up>up>joachim.krieger@epfl.ch" class="auth_mailup> ; Wilhelm Schlagup>bup>up> ; up>up>schlag@math.uchicago.edu" class="auth_mailup>
• 关键词：Energy critical wave equation ; Finite time blow up ; Dynamical rescaling
• 刊名：Journal des Mathematiques Pures et Appliquees
• 出版年：June 2014
• 年：2014
• 卷：101
• 期：6
• 页码：873-900
• 全文大小：377 K

文摘

For the critical focusing wave equation upport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021782413001323&_mathId=si1.gif&_user=111111111&_pii=S0021782413001323&_rdoc=1&_issn=00217824&md5=ff2082423e90f7284fb5dc90f59af5e3" title="Click to view the MathML source">鈻=uup>5up> on upport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021782413001323&_mathId=si2.gif&_user=111111111&_pii=S0021782413001323&_rdoc=1&_issn=00217824&md5=b6668ec293822fe5783f59306d93b137" title="Click to view the MathML source">Rup>3+1up> in the radial case, we prove the existence of type II blow up solutions with scaling parameter upport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021782413001323&_mathId=si3.gif&_user=111111111&_pii=S0021782413001323&_rdoc=1&_issn=00217824&md5=f8b6117fdad321bd438b6e6fa1985696" title="Click to view the MathML source">位(t)=tup>−1−谓up> for all upport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021782413001323&_mathId=si4.gif&_user=111111111&_pii=S0021782413001323&_rdoc=1&_issn=00217824&md5=bdecb699acef3f387f08f3f3c8826bee" title="Click to view the MathML source">谓>0$谓>0$. This extends the previous work by the authors and Tataru where the condition ii=S0021782413001323&_rdoc=1&_issn=00217824&md5=3bef3b4f4703ecdccf1f9ed69aee65fd">$谓>\frac{1}{2}$ had been imposed, and gives the optimal range of polynomial blow up rates in light of recent work by Duyckaerts, Kenig and Merle.