Bubble towers in the ancient solution of energy-critical heat equation

Abstract

We construct a radially smooth positive ancient solution for energy critical semi-linear heat equation in ${\mathbb{R}}^n$, $n\ge 7$. It blows up at the origin with the profile of multiple Talenti bubbles in the backward time infinity.

arXiv comment45 pages; comments welcome

References in corpus (3)

• Two-bubble dynamics for threshold solutions to the wave maps equation
• Construction of two-bubble solutions for the energy-critical NLS
• Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equation