7 citations · 23 across the 14 of their papers we have counts for
15 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 \[ u_t=Δu+u^3, \qquad n\geq 5. \] 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} Δv = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\ma…
Finite-time singularity formation for the heat flow of the -system
Yannick Sire, Juncheng Wei, Youquan Zheng +1
We construct the first example of finite time blow-up solutions for the heat flow of the -system, describing the evolution of surfaces with constant mean curvature \begin{equati…
Long-time dynamics for the energy critical heat equation in
Zaizheng Li, Qidi Zhang, Yifu Zhou +1
We investigate the long-time behavior of global solutions to the energy critical heat equation in \begin{equation*} \begin{cases} \pp_t u=Δu+|u|^{\frac{4}{3}} u ~&\mbox{ in }…
Global Existence of Weak Solutions to the Two Dimensional Nematic Liquid Crystal Flow with Partially Free Boundary
Yannick Sire, Yantao Wu, Yifu Zhou
We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in . We prove regularity estimates and the global existence of weak…
Trichotomy dynamics of the 1-equivariant harmonic map flow
Juncheng Wei, Qidi Zhang, Yifu Zhou
For the 1-equivariant harmonic map flow from into \begin{equation*} \left\{ \begin{aligned} &v_t=v_{rr}+\frac{v_r}{r} - \frac{\sin(2v)}{2r^2} , ~\quad(r,t)\in R_+\time…
On Fila-King Conjecture in Dimension Four
Juncheng Wei, Qidi Zhang, Yifu Zhou
We consider the following Cauchy problem for the four-dimensional energy critical heat equation \begin{equation*} \begin{cases} u_t=Δu+u^{3} ~&\mbox{ in }~ {\mathbb R}^4 \times (0,…
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(Δu+|\nabla u|^2u) -b…
Nematic liquid crystal flow with partially free boundary
Fanghua Lin, Yannick Sire, Juncheng Wei +1
We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes…
Global existence of free-energy solutions to the 2D Patlak--Keller--Segel--Navier--Stokes system with critical and subcritical mass
Chen-Chih Lai, Juncheng Wei, Yifu Zhou
We consider a coupled Patlak-Keller-Segel-Navier-Stokes system in that describes the collective motion of cells and fluid flow, where the cells are attracted by a ch…
New type II Finite time blow-up for the energy supercritical heat equation
Manuel del Pino, Chen-Chih Lai, Monica Musso +2
We consider the energy supercritical heat equation with the -th Sobolev exponent \begin{equation*} \begin{cases} u_t=Δu+u^{3},~&\mbox{ in } Ω\times (0,T),\\ u(x,t)=u|_{\part…
Finite time blow-up for the nematic liquid crystal flow in dimension two
Chen-Chih Lai, Fanghua Lin, Changyou Wang +2
We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain . Given any distinct points in the…
Infinite time blow-up for the fractional heat equation with critical exponent
M. Musso, Y. Sire, J. Wei +2
We consider positive solutions for the fractional heat equation with critical exponent \begin{equation*} \begin{cases} u_t = -(-Δ)^{s}u + u^{\frac{n+2s}{n-2s}}\text{ in } Ω\times (…