5 papers
Collapsing-tube type II blow-up for the energy-supercritical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei +1
We construct a new type II finite-time blow-up mechanism for the energy-supercritical heat equation \[ u_t=Îu+u^3, \qquad n\geq 5. \] The solution is positive and blows up only at…
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…
Multi-bubble solutions for the Dirichlet problem of the -system with higher degree
Xiang Fang, Juncheng Wei, Youquan Zheng +1
We consider a Dirichlet problem of the -system \begin{equation*} \begin{cases} Îv = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\m…
Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two
Juncheng Wei, Qidi Zhang, Yifu Zhou
We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert equation (LLG) from into \begin{equation*} \begin{cases} u_t= a(Îu+|\nabla u|^2u) -…