Interface boundary value problem for the Navier-Stokes equations in thin two-layer domains
The authors consider the Navier-Stokes equations in a thin two-layer domain \(\Omega_\varepsilon= \Gamma\times (0,\varepsilon)\cup \Gamma\times(-\varepsilon, 0)\), where \(\Gamma= (0,l_1)\times (0,l_2)\subset \mathbb{R}^2\). On the interface \(\Gamma\times \{0\}\), conditions are imposed which essentially how that there is no interaction between the fluids in vertical direction. The authors prove the global existence of strong solutions for large initial data and external forces (the size of which is related to \(\varepsilon\)). The system can be seen as a simplified model for atmosphere-ocean interaction.
scientific article; zbMATH DE number 2136541
scientific article