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arXiv · 2606.22384

Global Well-Posedness of sessile drop problem: 2D Navier-Stokes Flow

Xiaoding Yang
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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.

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Xiaoding Yang. 2026-06-21. Global Well-Posedness of sessile drop problem: 2D Navier-Stokes Flow. https://arxiv.org/abs/2606.22384

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