Related papers: A Solvability criterion for Navier-Stokes equation…
For barotropic compressible Navier-Stokes equations in three-dimensional (3D) bounded domains, we prove that any finite energy weak solution obtained by Lions [Mathematical topics in fluid mechanics, Vol. 2. Compressible models(1998)] and…
In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…
This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…
The Ladyzhenskaya-Smagorinsky equations model turbulence phenomena, and are given by $$\frac{\partial \boldsymbol{u}}{\partial t}-\mu…
We introduce a new modified Navier-Stokes model in $3$ dimensions by modifying the convection term in the ordinary Navier-Stokes equations. This is done by replacing the convective term $(\textbf{u}\cdot \nabla) \textbf{u}$ by…
This paper investigates an incompressible chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion \begin{eqnarray} \left\{\begin{array}{lll} n_t+u\cdot\nabla n=\nabla\cdot(|\nabla n|^{p-2}\nabla n)-\nabla\cdot(n\chi(c)\nabla c),&…
In this paper, we consider the generalized Navier-Stokes equations with fritional dissipation $(-\Delta)^{\beta}$ with $\beta>\frac{1}{2}$. When $\beta\in(1,2)$, We prove that smooth solutions of the generalized Navier-Stokes equations are…
We prove that the three-dimensional incompressible Navier-Stokes equations with the deformation Laplacian on hyperbolic 3-space $\HH^3$ admit a unique global mild solution for sufficiently small initial data in $L^3(\HH^3)$, and that this…
In this paper we study a well-known three--dimensional turbulence model, the filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES) tensor-diffusivity model of turbulent flows with an additional spatial filter of…
We study the low-energy solutions to the 3D compressible Navier-Stokes-Poisson equations. We first obtain the existence of smooth solutions with small $L^2$-norm and essentially bounded densities. No smallness assumption is imposed on the…
We study weak solutions of the 3D Navier-Stokes equations in whole space with $L^2$ initial data. It will be proved that $\nabla^\alpha u $ is locally integrable in space-time for any real $\alpha$ such that $1< \alpha <3$, which says that…
In this paper we consider the Navier-Stokes Equations in 3 dimensions in the vorticity formulation in the absence of the external forces. We derive upper bounds on L_{infinity} norm of omega and use them together with the Local Existence…
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in $\R^3$. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the $\alpha^{th}$-order fractional…
We study the dyadic model of the Navier-Stokes equations introduced by Katz and Pavlovi\'c. They showed a finite time blow-up in the case where the dissipation degree $\alpha$ is less than 1/4. In this paper we prove the existence of weak…
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. The underlying relative energy inequality holds as an equality for classical solutions and if the additional variable vanishes, these…
We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a…
In this paper we deal with the Cauchy problem for the hypodissipative Navier-Stokes equations in the three-dimensional periodic setting. For all Laplacian exponents $\theta<\frac13$, we prove non-uniqueness of dissipative $L^2_tH^\theta_x$…
In this paper, we derive an energy conservation criterion based on a combination of velocity and its gradient for the weak solutions of both the homogeneous incompressible Navier-Stokes equations and the general compressible Navier-Stokes…
This paper concerns the isentropic compressible Navier-Stokes equations in a three-dimensional (3D) bounded domain with slip boundary conditions and vacuum. It is shown that the classical solutions to the initial-boundary-value problem of…
This paper is devoted to the study of strong solutions for the compressible Navier-Stokes/Allen-Cahn system in bounded domain $\Omega\subset\mathbb R^3$, allowing for the presence of initial vacuum. A characteristic of this system is the…