Mathematics > Analysis of PDEs
arXiv:2606.22384 (math)
[Submitted on 21 Jun 2026]
Abstract:We prove the global well-posedness of small perturbations of two-dimensional sessile droplet equilibria for the incompressible Navier--Stokes equations with surface tension, Navier-slip boundary conditions, and a dynamic contact-point law. The main difficulty is the construction of solutions in the presence of the horizontal translational degeneracy of the equilibrium manifold. To remove this degeneracy, we work in a moving polar coordinate system determined by an orthogonality condition. We then establish local well-posedness through a Galerkin construction of pressureless weak solutions, recovery of the pressure, higher-order estimates, and a contraction argument. Combining this local theory with the global energy--dissipation estimates obtained in our previous work yields a unique global solution and the corresponding exponential decay estimate.
Submission history
From: Xiaoding Yang [view email]
[v1]
Sun, 21 Jun 2026 08:15:59 UTC (64 KB)
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

























