We review recent results on the global well-posedness and decay versus blow-up and non-decay dichotomy, below the stationary solution, for a focusing energy-critical heat equation in R4: Our methods are inspired by recent progress towards the soliton resolution conjecture for dispersive and wave equations, providing an alternative way of studying critical parabolic problems.
|Title of host publication||Nonlinear dispersive waves and fluids|
|Subtitle of host publication||AMS Proceedings in Contemporary Mathematics 2017-2018|
|Publisher||American Mathematical Society|
|Number of pages||15|
|Publication status||Accepted/In press - 4 Jul 2018|