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In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In partic
In this brief survey we outline the recent advances on the stability issues of certain finite time type II blow-up solutions for the energy critical focusing wave equation □u=−u5 in $\mathbb{
We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on R3+1 constructed in \cite{KST}, \cite{KS1} are stable along a co-dim