Brezis-Gallouet-Wainger type inequalities and a priori estimates of strong solutions to Navier-Stokes equations

2020 ◽  
Vol 278 (4) ◽  
pp. 108277
Author(s):  
Ryo Kanamaru
Keyword(s):  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates

The non-Lipschitz stochastic Cahn–Hilliard–Navier–Stokes equations in two space dimensions

2021 ◽  
pp. 2250003
Author(s):  
Chengfeng Sun ◽  
Qianqian Huang ◽  
Hui Liu
Keyword(s):  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates ◽  
Convergence Method ◽  
Two Space Dimensions ◽  
Lipschitz Conditions ◽  
Weak Convergence Method

The stochastic two-dimensional Cahn–Hilliard–Navier–Stokes equations under non-Lipschitz conditions are considered. This model consists of the Navier–Stokes equations controlling the velocity and the Cahn–Hilliard model controlling the phase parameters. By iterative techniques, a priori estimates and weak convergence method, the existence and uniqueness of an energy weak solution to the equations under non-Lipschitz conditions have been obtained.

scholarly journals REFINED A PRIORI ESTIMATES FOR THE AXISYMMETRIC NAVIER-STOKES EQUATIONS

2017 ◽  
Vol 7 (2) ◽  
pp. 554-558 ◽  
Author(s):  
Zujin Zhang ◽  
◽  
Xiqin Ouyang ◽  
Xian Yang ◽  
◽  
...  
Keyword(s):  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates

scholarly journals Maximum Norm Estimates of the Solution of the Navier-Stokes Equations in the Halfspace with Bounded Initial Data

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Santosh Pathak
Keyword(s):  
Initial Data ◽  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Maximum Norm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Norm Estimates ◽  
Priori Estimates ◽  
The Cauchy Problem

In this paper, I consider the Cauchy problem for the incompressible Navier-Stokes equations in ℝ + n for n ≥ 3 with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a continuation of my work in my previous papers, where the initial data are considered in T n and ℝ n respectively. In this paper, because of the nonempty boundary in our domain of interest, the details in obtaining the desired result are significantly different and more challenging than the work of my previous papers. This challenges arise due to the possible noncommutativity nature of the Leray projector with the derivatives in the direction of normal to the boundary of the domain of interest. Therefore, we only consider one derivative of the velocity field in that direction.

scholarly journals A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations with periodic initial data

2019 ◽  
Vol 36 (1-2) ◽  
pp. 39-50
Author(s):  
Santosh Pathak
Keyword(s):  
Initial Data ◽  
A Priori Estimates ◽  
Stokes Equations ◽  
A Priori ◽  
Maximum Norm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Periodic Initial Data

In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in Rn for n ≥ 3 with smooth periodic initial data and derive a priori estimtes of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a special case of a paper by H-O Kreiss and J. Lorenz which also generalizes the main result of their paper to higher dimension.

scholarly journals On the analysis of a geometrically selective turbulence model

2020 ◽  
Vol 9 (1) ◽  
pp. 1402-1419 ◽  
Author(s):  
Nejmeddine Chorfi ◽  
Mohamed Abdelwahed ◽  
Luigi C. Berselli
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Large Scale ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Smagorinsky Model ◽  
Navier Stokes Equations ◽  
Velocity Pressure

Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider regularized systems which are inspired by the Baldwin-Lomax and by the selective Smagorinsky model based on vorticity angles, and which can be interpreted as Large Scale methods for turbulent flows. We consider damping terms which are active at the level of the vorticity. We prove the main a priori estimates and compactness results which are needed to show existence of weak and/or strong solutions, both in velocity/pressure and velocity/vorticity formulation for various systems. We start with variants of the known ones, going later on to analyze the new proposed models.

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