A higher speed type II blow-up for the 4-d Fujita equation

Abstract

This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation $u_t=\Delta u+u^3$. Our main result is to show that the existence of type II blowup solutions, and $\Vert u(\cdot ,t){\Vert }_{\infty }\sim (T-t{)}^{-k}|ln(T-t){|}^{\frac{2k}{2k-1}},(k=1,2,3\cdots )$.The inner-outer gluing method has been employed.

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