OPTIMAL GEVREY STABILITY OF HYDROSTATIC APPROXIMATION FOR THE NAVIER-STOKES EQUATIONS IN A THIN DOMAIN
Chao Wang, Y.-G. Wang
Abstract
Abstract In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When we have convex initial data with Gevrey regularity of optimal index $\frac {3}{2}$ in the x variable and Sobolev regularity in the y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper being independent of $\varepsilon $ , by the same argument, we also obtain the well-posedness of the hydrostatic Navier-Stokes/Prandtl system in the optimal Gevrey space. Our results improve upon the Gevrey index of $\frac {9}{8}$ found in [15, 35].
Topics & Concepts
MathematicsSobolev spaceMathematical analysisNavier–Stokes equationsDomain (mathematical analysis)Stokes problemPrandtl numberVariable (mathematics)Hydrostatic equilibriumStability (learning theory)CompressibilityPhysicsThermodynamicsMachine learningComputer scienceFinite element methodHeat transferQuantum mechanicsNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential Equations