相关论文: Existence, regularity and uniqueness of weak solut…

In this paper, we prove the existence and a partial regularity of a weak solution to the system governing the interaction between a rigid body and a viscous incompressible Newtonian fluid. The evolution of the system body-fluid is studied…

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…

We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a…

We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution…

Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not…

We study the barotropic compressible Navier-Stokes system where the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. The system is subject to the…

It is known that uniqueness of mild solutions to the incompressible Navier-Stokes equations holds in the critical class $C([0,T);L^n(\mathbb{R}^n))$ for $n \geqslant 3$. In this paper, we prove that this result is sharp in the sense that…

A domain in $\mathbb{R}^3$ that touches the $x_3$ axis at one point is found with the following property. For any initial value in a $C^2$ class, the axially symmetric Navier Stokes equations with Navier slip boundary condition has a finite…

We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like…

We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with…

We prove some criteria for the convergence of weak solutions of the 2D incompressible Navier-Stokes equations with Navier slip boundary conditions to a strong solution of incompressible Euler. The slip rate depends on a power of the…

We show that if u is a weak solution to the Navier-Stokes initial-boundary value problem with Navier's slip boundary conditions in $Q_T:=\Omega\times(0,T)$, where $\Omega$ is a domain in $R^3$, then an associated pressure $p$ exists as a…

We prove that there exists a weak solution of the Stokes system with a non-zero external force and no-slip boundary conditions in a half space of dimensions three and higher so that its normal derivatives are unbounded near boundary. A…

The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface, despite the assumption of the no-slip condition is preferred to avoid boundary terms in the analysis…

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of…

This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain $(0,1)\times\mathbb{T}^2$ with a class of generalized slip boundary conditions that were systematically derived from…

A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are…

It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…

We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^\gamma$ for $\gamma\geq 9/5$ in three space dimension. The novelty of the paper is the approximation scheme…

We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding…