4 papers
Self-similar solutions of the three-dimensional Muskat problem with surface tension
Lizhe Wan, Jiaqi Yang
We construct a one-parameter family of small self-similar solutions to the three-dimensional one-phase Muskat problem with surface tension. The solutions have the form $η_\varepsi…
Nonlinear modulational instability of two-dimensional deep hydroelastic Stokes waves
Lizhe Wan, Jiaqi Yang
In this paper, we study the nonlinear modulational instability of two-dimensional hydroelastic Stokes waves in infinite depth. We first justify a focusing cubic nonlinear Schrödin…
On the well-posedness of two-dimensional Muskat problem with an elastic interface
Lizhe Wan, Jiaqi Yang
We investigate the two-dimensional Muskat problem with a nonlinear elastic interface, for both one-phase and two-phase scenarios. Following the framework developed by Nguyen [35,36…
Low regularity well-posedness for two-dimensional hydroelastic waves
Lizhe Wan, Jiaqi Yang
We investigate the low regularity local well-posedness of two-dimensional irrotational deep hydroelastic waves. Building on the approach of Ifrim-Tataru [29] and Ai-Ifrim-Tataru [5…