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We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly…

Analysis of PDEs · Mathematics 2018-12-31 Kyungkeun Kang , Hideyuki Miura , Tai-Peng Tsai

This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…

Analysis of PDEs · Mathematics 2025-03-07 Aseel Farhat , Anuj Kumar , Vincent R. Martinez

We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) elastic plate equation for in-plane motions on a flexible flat part of the boundary. The…

Analysis of PDEs · Mathematics 2020-07-15 Igor Chueshov

In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An…

Analysis of PDEs · Mathematics 2007-05-23 Thomas Y. Hou , Congming Li

In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak…

In this paper, we study the connectedness and compactness of the attainability set of weak solutions to the three-dimensional Navier--Stokes equations with damping. Depending on the value of the parameter \b{eta}, which controls the damping…

Analysis of PDEs · Mathematics 2025-07-31 Daniel Pardo , José Valero , Ángel Giménez

Time-periodic solutions to the Navier-Stokes equations that govern the flow of a viscous liquid past a three-dimensional body moving with a time-periodic velocity are investigated. The net motion of the body over a full time-period is…

Analysis of PDEs · Mathematics 2016-10-03 Giovanni P. Galdi , Mads Kyed

We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) elastic plate equation for transversal displacement on a flexible flat part of the…

Analysis of PDEs · Mathematics 2011-09-21 Igor Chueshov , Iryna Ryzhkova

In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform $C^2$-domains (not necessarily bounded), which obeys the scaling invariance principle, and prove the existence and uniqueness of strong solutions to this tamed equation.…

Analysis of PDEs · Mathematics 2008-06-11 Xicheng Zhang

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…

Analysis of PDEs · Mathematics 2021-03-30 Anthony Suen

This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…

Analysis of PDEs · Mathematics 2024-05-29 Young-Pil Choi , Houzhi Tang , Weiyuan Zou

The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…

Fluid Dynamics · Physics 2014-12-17 Fereidoun Sabetghadam

By applying Wiegner' method in \cite{Wiegner}, we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space…

Analysis of PDEs · Mathematics 2014-03-18 Jean-Yves Chemin , Ping Zhang

The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…

Analysis of PDEs · Mathematics 2008-08-28 David T. Purvance

Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…

Analysis of PDEs · Mathematics 2015-06-17 Mads Kyed

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. The dissipative character of our model…

Analysis of PDEs · Mathematics 2017-12-06 Francesco Di Plinio , Andrea Giorgini , Vittorino Pata , Roger Temam

The large time behavior of the unique strong solution to the barotropic compressible Navier-Stokes system is studied with large external forces and initial data, where the shear viscosity is a positive constant and the bulk one is…

Analysis of PDEs · Mathematics 2023-10-25 Xinyu Fan , Jing Li , Xue Wang

The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal variant consists of the Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-05-30 Sergio Frigeri , Maurizio Grasselli

Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible…

Analysis of PDEs · Mathematics 2021-05-24 Lan Zeng , Zhifei Zhang , Ruizhao Zi

The nonhomogeneous Navier-Stokes equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with nonslip or slip boundary conditions. We prove that the strong solutions exists globally in time provided…

Analysis of PDEs · Mathematics 2022-05-13 Guocai Cai , Boqiang Lü , Yi Peng