175 citations · 729 across the 112 of their papers we have counts for
137 papers
Parabolic defect measures for Harmonic Maps with Free Boundary
Anirban Das, Ali Hyder, Yannick Sire
We introduce defect measures for the heat flow of a class of harmonic maps with free boundary and initiate their analysis. Our flow is motivated by singular perturbations on the bo…
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 \[ (\partial_t-Δ)^σu = |u|^{p-1}u \quad \text{in } \mathbb{R}^n \times \mathbb{R}_{-}, \qquad 0 < σ< 1. \] For …
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…
Global oscillatory solutions for the Yang-Mills heat flow
Yannick Sire, Juncheng Wei, Youquan Zheng +1
We investigate the long-time dynamics for the global solution of the -equivariant Yang-Mills heat flow (YMHF) with structure group in space dimension . For a clas…
Liquid crystals and topological vorticity: smoothness of mild solutions
Fanghua Lin, Yannick Sire, Yantao Wu +1
We introduce several new models whose common feature is to take into account effects from topological vorticity. The macroscopic unknown is driven by a dissipative anomalous diffus…