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In this paper we investigate the inviscid limit $\nu \to 0$ for time-quasi-periodic solutions of the incompressible Navier-Stokes equations on the two-dimensional torus ${\mathbb T}^2$, with a small time-quasi-periodic external force. More…

Analysis of PDEs · Mathematics 2022-07-25 Luca Franzoi , Riccardo Montalto

The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the…

Analysis of PDEs · Mathematics 2022-05-03 Zhilei Liang , Apala Majumdar , Dehua Wang , Yixuan Wang

We develop the concept of an infinite-energy statistical solution to the Navier-Stokes and Euler equations in the whole plane. We use a velocity formulation with enough generality to encompass initial velocities having bounded vorticity,…

Analysis of PDEs · Mathematics 2015-05-13 James P. Kelliher

In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of…

Numerical Analysis · Mathematics 2024-08-21 Gabriel R. Barrenechea , Ernesto Castillo , Douglas R. Q. Pacheco

We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-dimensional moving closed surface as the width of the thin…

Analysis of PDEs · Mathematics 2017-10-10 Tatsu-Hiko Miura

This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…

Numerical Analysis · Mathematics 2025-12-25 Tim Brüers , Christoph Lehrenfeld , Max Wardetzky

We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $\Omega$. We show the convergence of the weak solution to the…

Analysis of PDEs · Mathematics 2022-07-26 Luca Bisconti , Matteo Caggio

Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier-Stokes model cannot account for both features, and a simple…

Fluid Dynamics · Physics 2025-07-04 C. Balitactac , C. Rodriguez

The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…

Numerical Analysis · Mathematics 2024-10-30 D. V. Lomasov , P. N. Vabishchevich

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…

Analysis of PDEs · Mathematics 2009-01-05 Gui-Qiang Chen , Zhongmin Qian

We establish local balance equations for smooth functions of the vorticity in the DiPerna-Majda weak solutions of 2D incompressible Euler, analogous to the balance proved by Duchon and Robert for kinetic energy in 3D. The anomalous term or…

Analysis of PDEs · Mathematics 2009-10-31 Gregory L. Eyink

There are a few examples of solutions to the incompressible Euler equations which are piecewise smooth with a discontinuity of the tangential velocity across a hypersurface evolving in time: the so-called vortex sheets. An important open…

Analysis of PDEs · Mathematics 2017-08-30 Franck Sueur

Consider the steady solution to the incompressible Euler equation $\bar u=Ae_1$ in the periodic tunnel $\Omega=\mathbb T^{d-1}\times(0,1)$ in dimension $d=2,3$. Consider now the family of solutions $u^\nu$ to the associated Navier-Stokes…

Analysis of PDEs · Mathematics 2023-08-30 Alexis F. Vasseur , Jincheng Yang

We consider the Euler equations of incompressible fluids and attempt to solve the initial value problem with the help of a concave maximization problem.We show that this problem, which shares a similar structure with the optimal transport…

Analysis of PDEs · Mathematics 2018-11-14 Yann Brenier

We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…

Probability · Mathematics 2023-08-16 Daniel Goodair , Dan Crisan

We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as…

Analysis of PDEs · Mathematics 2013-08-23 Mihaela Ignatova , Gautam Iyer , James P. Kelliher , Robert L. Pego , Arghir D. Zarnescu

The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class…

Analysis of PDEs · Mathematics 2025-06-10 Alessio Falocchi , Ana Leonor Silvestre , Gianmarco Sperone

The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…

Fluid Dynamics · Physics 2007-05-23 Milan Batista

We introduce a two time-scale scheme which allows to extend the method of minimizing movements to hyperbolic problems. This method is used to show the existence of weak solutions to a fluid-structure interaction problem between a nonlinear,…

Analysis of PDEs · Mathematics 2020-08-12 Barbora Benešová , Malte Kampschulte , Sebastian Schwarzacher

The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…

Analysis of PDEs · Mathematics 2026-05-21 Changfeng Gui , Chunjing Xie , Huan Xu