Speaker: 

Jun-Cheng Wei

Institution: 

UBC

Time: 

Monday, April 17, 2023 - 3:00pm to 4:00pm

Host: 

Location: 

RH306

In this talk I will  consider energy-critical nonlinear heat equation

$$ u_t=\Delta u+ u^{\frac{n+2}{n-2}}, u\geq 0 $$

We prove that for $n\geq 7$, any blow-up must be of Type I, i.e. the blow-up rate must be bounded by $(T-t)^{-\frac{n-2}{4}}$. The proof is built on several key ingredients: first we perform tangent ow analysis and study bubbling formation in this process; next we give a second order bubbling analysis in the multiplicity one case, where we use a reverse inner-outer gluing mechanism; finally, in the higher multiplicity case (bubbling tower/cluster), we develop Schoen's Harnack inequality and obtain next order estimates in Pohozaev identities for critical parabolic flows. (Joint work with Kelei Wang.)

The option to join via Zoom may be accessed through this link.