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This article is an updated version of the article that was published in the Electronic Journal of Differential Equations on 10. July 2010. Two footnotes have been added. One corrects a minor error not influencing the proof, the second is…

General Mathematics · Mathematics 2012-12-04 Jorma Jormakka

We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitable'' weak solution to the problem becomes a strong one…

Analysis of PDEs · Mathematics 2025-04-30 Xiangsheng Xu

The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity…

Numerical Analysis · Mathematics 2023-07-12 Thierry Gallouët , Raphaèle Herbin , Jean-Claude Latché , David Maltese

This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…

Analysis of PDEs · Mathematics 2025-03-04 Yinghua Li , Manrou Xie

We develop an efficient, unconditionally stable, variable step second order exponential time differencing scheme for the incompressible Navier Stokes equations in two and three spatial dimensions under periodic boundary conditions, together…

Numerical Analysis · Mathematics 2026-02-24 Haifeng Wang , Xiaoming Wang , Min Zhang

We show the existence and the regularity properties of the weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with variable viscosity coefficient, by analyzing a fourth-order nonlinear…

Analysis of PDEs · Mathematics 2022-05-09 Zihui He , Xian Liao

In this paper, we propose and analyze a temporally second-order accurate, fully discrete finite element method for the magnetohydrodynamic (MHD) equations. A modified Crank--Nicolson method is used to discretize the model and appropriate…

Numerical Analysis · Mathematics 2021-08-13 Cheng Wang , Jilu Wang , Zeyu Xia , Liwei Xu

In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model couples the incompressible Navier--Stokes equations with an…

Numerical Analysis · Mathematics 2025-12-30 Endre Süli , Dennis Trautwein

A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in…

Computational Physics · Physics 2021-06-04 Mohamed M. Kamra , Jabir Al-Salami , Changhong Hu

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

In this paper we study the stochastic Navier-Stokes equation with artificial compressibility. The main results of this work are the existence and uniqueness theorem for strong solutions and the limit to incompressible flow. These results…

Probability · Mathematics 2010-12-07 Utpal Manna , Jose-Luis Menaldi , Sivaguru S. Sritharan

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…

Analysis of PDEs · Mathematics 2012-12-18 Jingchi Huang , Marius Paicu , Ping Zhang

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and…

Numerical Analysis · Mathematics 2018-05-15 Alexander Lozovskiy , Maxim A. Olshanskii , Yuri V. Vassilevski

Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the…

Numerical Analysis · Mathematics 2019-04-12 Philipp W. Schroeder , Christoph Lehrenfeld , Alexander Linke , Gert Lube

A new iterative projection method is proposed to solve the unsteady Navier-Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence free space only once…

Numerical Analysis · Mathematics 2025-10-02 Xiaoming Zheng , Kun Zhao , Jiahong Wu , Weiwei Hu , Dapeng Du

The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objects. Despite the simplicity, the method is typically limited…

Numerical Analysis · Mathematics 2014-02-12 David Shirokoff , Jean-Christophe Nave

A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…

Numerical Analysis · Mathematics 2014-11-27 F. Guillén-González , M. V. Redondo-Neble

In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.

Analysis of PDEs · Mathematics 2018-09-26 Xiaopeng Zhao , Haichao Meng

This paper considers the backward Euler based linear time filtering method for the EMAC formulation of the incompressible Navier-Stokes equations. The time filtering is added as a modular step to the standard backward Euler code leading to…

Numerical Analysis · Mathematics 2022-03-11 Medine Demir , Aytekin Çıbık , Songül Kaya

The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…

Numerical Analysis · Mathematics 2026-02-09 María Gabriela Armentano , Mauricio Mendiluce