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We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…

Optimization and Control · Mathematics 2024-07-10 Oscar A. Holroyd , Radu Cimpeanu , Susana N. Gomes

We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures.

Analysis of PDEs · Mathematics 2017-09-04 Diego Chamorro , Pierre Gilles Lemarié-Rieusset , Kawther Mayoufi

Error bounds for fully discrete schemes for the evolutionary incompressible Navier--Stokes equations are derived in this paper. For the time integration we apply BDF-$q$ methods, $q\le 5$, for which error bounds for $q\ge 3$ cannot be found…

Numerical Analysis · Mathematics 2025-06-23 Bosco García-Archilla , V. John , Julia Novo

This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…

Fluid Dynamics · Physics 2024-11-08 Rômulo Damasclin Chaves dos Santos

First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with $L^2$ initial data in convex polygonal domains, without extra regularity…

Numerical Analysis · Mathematics 2021-01-19 Buyang Li , Shu Ma , Yuki Ueda

In the present work we show some results on the effect of the Smagorinsky model on the stability of the associated perturbation equation. We show that in the presence of a spectral gap, such that the flow can be decomposed in a large scale…

Numerical Analysis · Mathematics 2021-12-01 Erik Burman , Peter Hansbo , Mats G. Larson

We study convergence of a mixed finite element-finite volume scheme for the compressible Navier Stokes equations in the isentropic regime under the full range of the adiabatic coefficient gamma for the problem with general non zero…

Numerical Analysis · Mathematics 2020-05-05 Young-Sam Kwon , Antonin Novotny

We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value…

Mathematical Physics · Physics 2017-12-29 Sergei Kuksin , Armen Shirikyan

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…

Numerical Analysis · Mathematics 2013-07-17 M. Kovács , S. Larsson , F. Lindgren

Statistical solutions, which are time-parameterized probability measures on spaces of square-integrable functions, have been established as a suitable framework for global solutions of incompressible Navier-Stokes equations (NSE). We…

Numerical Analysis · Mathematics 2021-07-14 Pratyuksh Bansal

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Fluid Dynamics · Physics 2024-05-31 Matteo Zancanaro , Valentin Nkana Ngan , Giovanni Stabile , Gianluigi Rozza

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…

Numerical Analysis · Mathematics 2023-10-09 Julius Jeßberger , Alex Kaltenbach

For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximations. These…

Numerical Analysis · Mathematics 2019-03-01 Shun Zhang

The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and three dimensions. It is shown that the density keeps strictly…

Analysis of PDEs · Mathematics 2022-04-27 Zhilei Liang

For linearized Navier-Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauchy problem and finally we prove conditional stability…

Analysis of PDEs · Mathematics 2022-07-06 Oleg Y. Imanuvilov , Luca Lorenzi , M. Yamamoto

The Volume-Averaged Navier-Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high-order finite element solver using both forms A and B of these equations.…

Numerical Analysis · Mathematics 2023-02-20 Toni El Geitani , Shahab Golshan , Bruno Blais

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…

Analysis of PDEs · Mathematics 2026-04-08 Chao Wang , Jingchao Yue , Zhifei Zhang

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the…

Numerical Analysis · Mathematics 2017-07-06 Jean-Claude Latché , Khaled Saleh

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…

Fluid Dynamics · Physics 2015-06-23 Matteo Parsani , Mark H. Carpenter , Eric J. Nielsen

In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals in the independent variables. The notion of strong…

Analysis of PDEs · Mathematics 2012-05-01 Vladimir P. Gerdt