| Abstract: |
| We address the blow-up rate issue for the Nonlinear Wave Equation (NLW) with superlinear power nonlinearity. For subconformal and conformal power, the blow-up rate is given by the solution of the associated ODE, as this was shown by Merle and Zaag in 2003 and 2005. In the superconformal case below the Sobolev exponent, various bounds are known, from the work of Killip, Stovall and Visan in 2014, and also in our earlier paper in 2013. The aim of this talk is to give a better bound. Our method relies on some energy estimates in similarity variables, where we consider the superconformal case as a (large) perturbation of the conformal case. This leads to some exponential bound on the self-similar version, directly related to the size of the large perturbation. |
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