相关论文: Gluing non-unique Navier-Stokes solutions

In some problems of fluid mechanics, it is possible to be confronted with data that are not regular, that is why we are interested here in the search for the so-called very weak solutions for the stationary Stokes problem with Navier-type…

We prove unique existence of mild solutions on $L^{\infty}_{\sigma}$ for the Navier-Stokes equations in an exterior domain in $ \mathbb{R}^{n}$, $n\geq 2$, subject to the non-slip boundary condition.

We discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear…

In this paper we propose new method for proving of global solutions for 3D Navier-Stokes equations. This complies an application to the Clay Institute Millennium Prize Navier Stokes Problem. The proposed method can be applied for…

In this article the question on uniqueness of weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case is studied. Here the investigation is carried out with use of another approach. The uniqueness of velocity…

In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type…

Recently, strong evidence has accumulated that some solutions to the Navier-Stokes equations in physically meaningful classes are not unique. The primary purpose of this paper is to establish necessary properties for the error of…

A proof is given of the global existence and uniqueness of a weak solution to Navier-Stokes boundary problem. The proof is short and essentially self-contained.

We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong…

Using ODE-methods and trapping regions derived by Mattingly and Sinai we give a new proof of the existence and uniqueness of solutions to Navier-Stokes equations with periodic boundary conditions on the plane.

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…

In this paper, we investigate the Leray problem for steady Navier-Stokes system under full slip boundary conditions in a two dimensional channel with straight outlets. The existence of solutions with arbitrary flux in a general channel with…

Let $\bfu$ be a Leray solution to the Navier-Stokes boundary-value problem in an exterior domain, vanishing at infinity and satisfying the generalized energy inequality. We show that if there exist $R>0$ and ${\sf s}\ge \frac23 q$, $q>6$,…

In this paper, we extend considerably the global existence results of entropy-weak solutions related to compressible Navier-Stokes system with density dependent viscosities obtained, independently (using different strategies), by Vasseur-Yu…

Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…

Based on Leray's formulation of the Navier-Stokes equations and the conditions of the exact linear representation of the nonlinear problem found in this paper, a compact explicit expression for the exact operator solution of the…

In this paper we consider the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces $X$ and $Y$, respectively, to be the…

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants,…

In the first part of this article, we obtain a linear system whose the solution solves the time-independent incompressible Navier-Stokes system for the special case in which the external forces vector is a gradient. In a second step we…

In this paper we show the non-uniqueness of mild solutions to the two-dimensional forced Navier-Stokes equations in the half space under the noslip boundary condition, following the program established by Albritton, Bru{\'e}, and Colombo in…