Related papers: Analyticity estimates for the Navier-Stokes equati…
In the present paper, we consider the real analyticity of the global solutions to the $3$D incompressible anisotropic Navier--Stokes equations. We show that if only the horizontal component of initial velocity is small and analytic in…
Fundamental solutions to the time-periodic Stokes and Oseen linearizations of the Navier-Stokes equations in dimension $n\geq 2$ are investigated. Integrability properties and pointwise estimates are established.
We establish a new Liouville-type theorem for the stationary Navier--Stokes equations in $\mathbb{R}^3$. The main result is an improvement of the previous result with a logarithmic factor based on an understanding of $L^p$ growth of the…
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…
We consider the nonstationary linearized Navier-Stokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the…
These notes are dedicated to the analysis of the one-dimensional free-congested Navier-Stokes equations. After a brief synthesis of the results obtained in [4] related to the existence and the asymptotic stability of partially congested…
The axially symmetric solutions to the Navier-Stokes equations in a periodic cylinder with boundary slip conditions on the lateral part of its boundary are considered. A priori estimates for solutions with large swirl necessary for a proof…
We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…
Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…
We investigate regularity estimates for the stationary Navier-Stokes equations above a highly oscillating Lipschitz boundary with the no-slip boundary condition. Our main result is an improved Lipschitz regularity estimate at scales larger…
We prove existence of global-in-time weak solutions of the incompressible Navier-Stokes equations in the half-space $\mathbb{R}^3_+$ with initial data in a weighted space that allow non-uniformly locally square integrable functions that…
This short proof shows that for smooth and sufficiently fast decaying initial data at infinity, the full incompressible Navier-Stokes solutions are eternal. The proof uses an orthogonal decomposition of the velocity field and some…
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…
Relativistic Navier-Stokes equations express the conservation of the energy-momentum tensor and the particle number current in terms of the local hydrodynamic variables: temperature, fluid velocity, and the chemical potential. We show that…
In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the…
We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…
We introduce a modification of the Navier-Stokes equation that has the remarkable property of possessing an infinite number of conserved quantities in the inviscid limit. This new equation is studied numerically and turbulence properties…
The Navier-Stokes equations, which govern fluid motions, are not resolved yet. This investigation relates to the application of the power series method to the incompressible Navier-Stokes equations. This method involves replacing variables…
The existence, uniqueness and uniformly estimates for solutions of the parameter dependent abstract Navier-Stokes problem on half space are derived. In application the existence, uniqueness and uniformly L^{p} estimates for solution of the…
In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the…