Stability in the Stefan problem with surface tension (II)

Details Stability in the Stefan problem with surface tension (II) Stability in the Stefan problem with surface tension (II)

2009-05-22

arxiv.org/abs/0905.3600v1

Mathematics

Analysis of PDEs

76 pages

Scientific paper

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.

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