Gevrey class regularity for steady-state incompressible Navier-Stokes equations in parametric domains and related models

2025/04/18 by Chernov, Alexey, Le, Tung · 1 citation
#35Q30 #65C30 #65D30 #65D32 #65N30 #FOS: Mathematics #G.1.4 #G.1.8 #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2504.13753

Abstract

We investigate parameteric Navier-Stokes equations for a viscous, incompressible flow in bounded domains. The coefficients of the equations are perturbed by high-dimensional random parameters, this fits in particular for modelling flows in domains with uncertain perturbations. Our focus is on deriving bounds for arbitrary high-order derivatives of the pressure and the velocity fields with respect to the random parameters in the context of incompressible Navier-Stokes equation under a small-data assumption. To achieve this, we analyze mixed and saddle-point problems and employ the alternative-to-factorial technique to establish generalized Gevrey-class regularity for the solution pair. Thereby the analytic regularity follows as a special case. In the numerical experiments, we validate and illustrate our theoretical findings using Gauss-Legendre quadrature and Quasi-Monte Carlo methods.

Citations

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