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Finite energy Navier-Stokes flows with unbounded gradients induced by localized flux in the half-space
Kyungkeun Kang, Baishun Lai, Chen-Chih Lai +1
For the Stokes system in the half space, Kang [Math.~Ann.~2005] showed that a solution generated by a compactly supported, Hölder continuous boundary flux may have unbounded normal…
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…