相关论文: Some examples of singular fluid flows
We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described…
Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier--Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source)…
We consider the Navier-Stokes system solution, based at parametric representation of desired function. This solution is unique and it show the velocity of a stream element as its density structure [{\rho}_S (x,y,z,t);{\rho}^\to_L (x,y,z,t)]…
We consider a family of Leray-$\alpha$ models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter $\theta$, of the Navier-Stokes equations. In particular, they share…
Cahn-Hilliard-Navier-Stokes system describes the evolution of two isothermal, incompressible, immiscible fluids in a bounded domain. In this work, we consider the stationary nonlocal Cahn-Hilliard-Navier-Stokes system in two and three…
The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…
In this note we investigate the existence of time-periodic solutions to the $p$-Navier-Stokes system in the singular case of $p\in (1, 2)$, that describes the flows of an incompressible shear-thinning fluid. In the $3D$ space-periodic…
The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…
We consider the Navier-Stokes equations in $\mathbb{R}^3$ subject to the initial condition with initial velocity field in $L^{2}_{\rm loc} (\mathbb{R}^3)$ such that $\limsup_{R \to +\infty } R^{-1} \|u_{0} \|_{ L^{2}(B(R))} < +\infty$. Our…
We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and that the initial…
Regularity properties of strong solutions are considered.
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…
For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the solution is regular. Roughly speaking this implies that, near…
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…
We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged…
An algorithm for generating a class of closed form solutions to the Navier-Stokes equations is suggested, with examples. Of particular interest are those exact solutions that exhibit intermittency, tertiary Hopf bifurcations, flow reversal,…
The heat conducting compressible viscous flows are governed by the Navier-Stokes-Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat transfer at the boundary. On one part of…
We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…