Gevrey class regularity for steady-state incompressible Navier-Stokes equations in parametric domains and related models
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910914116059136 |
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| author | Chernov, Alexey Le, Tung |
| author_facet | Chernov, Alexey Le, Tung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13753 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gevrey class regularity for steady-state incompressible Navier-Stokes equations in parametric domains and related models Chernov, Alexey Le, Tung Numerical Analysis 35Q30, 65C30, 65D30, 65D32, 65N30 G.1.8; G.1.4 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. |
| title | Gevrey class regularity for steady-state incompressible Navier-Stokes equations in parametric domains and related models |
| topic | Numerical Analysis 35Q30, 65C30, 65D30, 65D32, 65N30 G.1.8; G.1.4 |
| url | https://arxiv.org/abs/2504.13753 |