Philipp Lohrmann
We estimate the inertial force field in the 3d Euler/Navier-Stokes equation in function of |u|_\infty and |\nabla u |_\infty and provide an application to the well-posed problem
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Limit behaviors of blow up solutions for impressible Navier-Stokes equations are obtained.
Weak solutions of incompressible Navier-Stokes Equations re-obtained variationally
In this paper, we continue the discussion as done in \cite{CTZ15} on turbulent channel flow described by the Navier-Stokes model and the Navier-Stokes-alpha model. We study the non-stationary solutions for the Navier-Stokes equations and Navier-Stokes-$α$ model having particular function forms. In particular, the term of sum of pressure and potential can be shown to be harmonic in the space variable.
In a series of papers (see \cite{CDT02} and the pertinent references therein) the 3D Navier-Stokes-$α$ model were shown to be a useful complement to the 3D Navier-Stokes equations; and in particular, to be a good Reynolds version of the latter equations. In this work, we introduce a simple Reynolds averaging which, due to the wall roughness, transforms the Navier-Stokes equations into the Navier-Stokes-$α$ model.
This note shows the blow-up of certain non-small solutions to relaxed compressible Navier-Stokes equations in divergence form.
The aim of this paper is to solve the three dimensional Navier-Stokes problem with conservative source term. We use convolution methods to construct "well behaved" smooth solutions of the initial boundary value problem for the system of Navier-Stokes with conservative source term.
Navier-Stokes Equations in Complex Space
研究复空间中Navier-Stokes方程的解，证明了其整体时间正则性。
With the previous results for the analytical blowup solutions of the N-dimensional Euler-Poisson equations, we extend the similar structure to construct an analytical family of solutions for the isothermal Navier-Stokes equations and pressureless Navier-Stokes equations with density-dependent viscosity.
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 Reynolds number, and it is increasingly apparent that the power 1 may be critical for L^2 convergence, as hinted at in [hal-01093331].
In this paper we consider the three-dimensional Navier-Stokes equations in an infinite channel. We provide a sufficient condition, in terms of $\partial_z p$, where $p$ is the pressure, for the global existence of the strong solutions to the three-dimensional Navier-Stokes equations.
We investigate the long-term dynamics of the three-dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid. Specifically, we derive upper bounds for the number of determining modes for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view we consider the Navier-Stokes-Voight model as a non-viscous (inviscid) regularization of the three-dimensional Navier-Stokes equations. Furthermore, we also show that the weak solutions of the Navier-Stokes-Voight equat…
The authors prove a maximum modulus estimate for solutions of the stationary Navier-Stokes system in bounded domains of polyhedral type.
We study spatial analyticity properties of solutions of the Navier-Stokes equations and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equations with data in H^r, r greater or equal 1/2, and prove a stability result for the analyticity radius.
In this paper we establish a Serrin type regularity criterion on the gradient of pressure in weak spaces for the Leray-Hopf weak solutions of the Navier-Stokes equations in R3.
This paper was removed by arXiv admin because it plagiarizes "Kozono, Hideo; Shimada, Yukihiro Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations. Math. Nachr. 276 (2004), 63--74."
We study the 4-dimensional pressureless Navier--Stokes-Poisson equations with density-dependent viscosity. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper.
We consider the interior regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case L^2_w(0,T;L^\infty(R^3)). Particularly, an open problem proposed in [KK] was solved.
We prove that the energy equality holds for weak solutions of the 3D Navier-Stokes equations in the functional class $L^3([0,T);V^{5/6})$, where $V^{5/6}$ is the domain of the fractional power of the Stokes operator $A^{5/12}$.
An upper bound of blow up rate for the Navier-Stokes equations with small data in L^2(R^3) is obtained.
We consider stochastic Navier-Stokes equations in a 2D-bounded domain with the Navier with friction boundary condition. We establish the existence and the uniqueness of the solutions and study the vanishing viscosity limit. More precisely, we prove that solutions of stochastic Navier-Stokes equations converge, as the viscosity goes to zero, to solutions of the corresponding stochastic Euler equations.
Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.
The Navier-Stokes-Voigt model of viscoelastic incompressible fluid has been recently proposed as a regularization of the three-dimensional Navier-Stokes equations for the purpose of direct numerical simulations. Besides the kinematic viscosity parameter, $ν>0$, this model possesses a regularizing parameter, $α> 0$, a given length scale parameter, so that $\frac{α^2}ν$ is the relaxation time of the viscoelastic fluid. In this work, we derive several statistical properties of the invariant measures associated with the solutions of the three-dimensional Navier-Stokes-Voigt equations. Moreover, we…
We study the regularity criteria for weak solutions to the $3D$ incompressible Navier--Stokes equations in terms of the geometry of vortex structures, taking into account the boundary effects. A boundary regularity theorem is proved on regular domains with a class of oblique derivative boundary conditions, providing that the vorticity of the fluid is coherently aligned. In particular, we establish the boundary regularity on round balls, half-spaces and right circular cylindrical ducts, subject to the classical Navier and kinematic boundary conditions.
We study some particular solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure, in radial symmetry. With extension of the previous known blowup solutions for the Euler-Poisson equations / pressureless Navier-Stokes-Poisson with density-dependent viscosity, we constructed the corresponding analytical blowup solutions for the Navier-Stokes-Poisson Equations with density-dependent viscosity and with pressure.
This is a rather comprehensive study on the dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes operator, (b). heteroclinics conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Besides Navier-Stokes and Euler equations, we also study two models of them.
This paper gives out the solution of divergent Navier-Stokes equations, and shows that in this case, under a physicalacceptable condition, the solution would be smooth .
A Navier--Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier--Stokes system. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations.
Reynolds Averaged Solutions of the Navier-Stokes Equation
本文证明一般初始条件下Navier-Stokes方程Young测度解的均值属于Leray-Hopf类PDE解。
General considerations on the Equivalence conjectures and a review of few mathematical results.
Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.
Multi-dimensional Jordan chain is presented. It is shown that it admits the finite-component reductions to the Navier-Stokes equation and other important equations of continuous media theory.
Some implications of the simplest accounting of defects of compatibility in the velocity field on the structure of the classical Navier-Stokes equations are explored, leading to connections between classical elasticity, the elastic theory of defects, plasticity theory, and classical fluid mechanics.
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