Abstract

We study a mathematical model for a compressible liquid in a capillary tube. We establish necessary and suficient conditions for existence and for uniqueness or near uniqueness of solutions, and we provide general height estimates for solutions, depending on the geometrical structure of the definition domain. We show that solutions exhibit discontinuous dependence properties in domains with corners, analogous to those that are known for the classical capillarity equation.

Keywords

capillary surfaces, capillary tube, mean curvature, compressible fluid, elliptic nonlinear second-order PDE

Mathematical Subject Classification

Primary: 76B45, 35J20, 53A10

Authors