Stability in the Stefan problem with surface tension (II)
نویسنده
چکیده
Continuing our study of the Stefan problem with surface tension effect, in this paper, we establish sharp nonlinear stability and instability of steady circles. Our nonlinear stability proof relies on an energy method along the moving domain, and the discovery of a new ‘momentum conservation law’. Our nonlinear instability proof relies on a variational framework which leads to the sharp growth rate estimate for the linearized problem, as well as a bootstrap framework to overcome the nonlinear perturbation with severe high-order derivatives.
منابع مشابه
Stability in the Stefan problem with surface tension (I)
We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension also known as the Stefan problem with Gibbs-Thomson correction.
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