11 papers
Giga-Kohn-type results for the fully fractional heat equation
Yannick Sire, Juncheng Wei, Ke Wu +1
We consider the semilinear fully fractional heat equation \[ (\partial_t-Î)^Ïu = |u|^{p-1}u \quad \text{in } \mathbb{R}^n \times \mathbb{R}_{-}, \qquad 0 < Ï< 1. \] For $n\leq 2…
Infinite time bubbling for the Yang-Mills heat flow on
Yannick Sire, Juncheng Wei, Youquan Zheng
We investigate the long time behaviour of the Yang-Mills heat flow on the bundle . Waldron \cite{Waldron2019} proved global existence and smoothness of th…
Singular set estimates for solutions to elliptic equations in higher co-dimension
Max Engelstein, Cole Jeznach, Yannick Sire
Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good unders…
Heat flow of harmonic maps into CAT()-spaces
Fang-Hua Lin, Antonio Segatti, Yannick Sire +1
We introduce a new approach to prove the global existence and uniqueness of suitable weak solutions of the heat flow of harmonic mappings into CAT(0) metric spaces. Our method allo…
Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy
Thomas Y. Hou, Xiang Qin, Yannick Sire +1
We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space and on the upper half-plane $\…
Fine regularity of fractional harmonic maps and applications
Kyeongbae Kim, Simon Nowak, Yannick Sire
In this paper, we derive several regularity results for harmonic mappings into Euclidean spheres associated with rather general energies related to fractional Sobolev spaces. These…