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Related papers: Well-posedness of the hydrostatic Navier-Stokes eq…

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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

In this paper, we study local regularity of the solutions to the Stokes equations near a curved boundary under no-slip or Navier boundary conditions. We extend previous boundary estimates near a flat boundary to that near a curved boundary,…

Analysis of PDEs · Mathematics 2025-10-23 Hui Chen , Su Liang , Tai-Peng Tsai

This work is devoted to the well-posedness issue for the low-Mach number limit system obtained from the full compressible Navier-Stokes system, in the whole space. In the case where the initial temperature (or density) is close to a…

Analysis of PDEs · Mathematics 2012-02-02 Raphaël Danchin , Xian Liao

We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…

Analysis of PDEs · Mathematics 2019-07-23 Wojciech M. Zajaczkowski

In this paper, we are concerned with the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space…

Analysis of PDEs · Mathematics 2024-01-19 Dongjuan Niu , Lu Wang

Heuristic derivations of the Navier-Stokes equations are unable to reveal the applicability limits of these equations. In this paper we rederive the Navier-Stokes equations from kinetic theory, using a method that affords a step by step…

Fluid Dynamics · Physics 2020-04-14 Peter Stubbe

We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we…

Soft Condensed Matter · Physics 2015-04-10 Jonasz Słomka , Jörn Dunkel

The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and Hemisphere, and in 3D for the Rectangle. The cases of the 2D…

Analysis of PDEs · Mathematics 2017-08-02 Duy Phan , Sérgio S. Rodrigues

In this manuscript, we study the theory of conformal relativistic viscous hydrodynamics introduced in arXiv:1708.06255, which provided a causal and stable first-order theory of relativistic fluids with viscosity. The local well-posedness of…

Analysis of PDEs · Mathematics 2019-11-07 Fabio S. Bemfica , Marcelo M. Disconzi , Casey Rodriguez , Yuanzhen Shao

We establish the global well-posedness for two-dimensional inhomogeneous, incompressible, anisotropic Navier-Stokes systems. Two specific models are analyzed: one with partial dissipation (referred to as (AINS)) and one with only horizontal…

Analysis of PDEs · Mathematics 2026-03-18 Hammadi Abidi , Guilong Gui , Ping Zhang

The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…

Analysis of PDEs · Mathematics 2019-02-28 I. S. Ciuperca , E. Feireisl , M. Jai , A. Petrov

We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the…

Probability · Mathematics 2019-04-22 Martina Hofmanova , James-Michael Leahy , Torstein Nilssen

We analyse the well posedness of a stochastic hyperviscosity-regularized 3D Navier-Stokes equation; this is the Navier-Stokes equation in which the Laplace operator is replaced by its a-power for a>1. We prove existence and uniqueness for…

Analysis of PDEs · Mathematics 2010-03-01 B. Ferrario

We study the Stokes system with the localized boundary data in the half-space. We are concerned with the local regularity of its solution near the boundary away from the support of the given boundary data which are product forms of each…

Analysis of PDEs · Mathematics 2023-07-06 Kyungkeun Kang , Chanhong Min

In this work, we proved the existence of a unique global mild solution of the d-dimensional incompressible Navier-Stokes equations, for small initial data in Besov type spaces based on mixed-Lebesgue spaces; namely, mixed-norm…

Analysis of PDEs · Mathematics 2025-03-21 Leithold L. Aurazo-Alvarez , Wladimir Neves

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…

Numerical Analysis · Mathematics 2025-04-21 Alexey Chernov , Tung Le

Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…

Analysis of PDEs · Mathematics 2026-02-12 Buddhika Priyasad , Sérgio S. Rodrigues

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^{\alpha}u &= \theta e_{2} \partial_{t}\theta+u\cdot\nabla \theta+ |D|^{\beta}\theta &=0 \quad with $\textrm{div} u=0$ and…

Analysis of PDEs · Mathematics 2011-12-20 Changxing Miao , Liutang Xue

In this paper, we establish the global existence of small solutions to the inhomogeneous Navier-Stokes system in the half-space. The initial density only has to be bounded and close enough to a positive constant, and the initial velocity…

Analysis of PDEs · Mathematics 2013-10-08 Raphael Danchin , Ping Zhang

This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data…

Analysis of PDEs · Mathematics 2013-04-23 Walter Craig , Xiangdi Huang , Yun Wang