arXiv subjects
Publications and source records attributed to J. Li.
Let $M$ be a compact Riemann surface, $h(x)$ a positive smooth function on $M$. In this paper, we consider the functional $$J(u)={1/2}\int \sb{M}|\bigtriangledown u|\sp 2 + 8π\int\sb{M}u -8π\log\int\sb{M}h\exp {u}$$. We give a sufficient condition under which $J$ achieves its minimum.
Extending work of Caffarelli-Yang and Tarantello, we present a variational existence proof for two-vortex solutions of the periodic Chern-Simons Higgs model and analyze the asymptotic behavior of these solutions as the parameter coupling the gauge field with the scalar field tends to 0.
Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation. The numerical modelling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Preliminary results concerning the time evolution of the liquid-gas interface and the vorticity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles.