scholarly journals Publisher's Note: Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations [Phys. Rev. E 94, 063103 (2016)]

2017 ◽  
Vol 95 (1) ◽  
Author(s):  
John D. Gibbon ◽  
Nairita Pal ◽  
Anupam Gupta ◽  
Rahul Pandit
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals A Geometrical Regularity Criterion in Terms of Velocity Profiles for the Three-Dimensional Navier–Stokes Equations

2019 ◽  
Vol 72 (4) ◽  
pp. 545-562 ◽  
Author(s):  
C V Tran ◽  
X Yu
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Velocity Profiles ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Velocity ◽  
Whole Space ◽  
Velocity Region

Summary In this article, we present a new kind of regularity criteria for the global well-posedness problem of the three-dimensional Navier–Stokes equations in the whole space. The novelty of the new results is that they involve only the profiles of the magnitude of the velocity. One particular consequence of our theorem is as follows. If for every fixed $t\in (0,T)$, the ‘large velocity’ region $\Omega:=\{(x,t)\mid |u(x,t)|>C(q)\left|\mkern-2mu\left|{u}\right|\mkern-2mu\right|_{L^{3q-6}}\}$, for some $C(q)$ appropriately defined, shrinks fast enough as $q\nearrow \infty$, then the solution remains regular beyond $T$. We examine and discuss velocity profiles satisfying our criterion. It remains to be seen whether these profiles are typical of general Navier–Stokes flows.

scholarly journals Remarks on the Regularity Criterion of the Navier-Stokes Equations with Nonlinear Damping

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Weihua Wang ◽  
Guopeng Zhou
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Nonlinear Damping ◽  
Navier Stokes ◽  
Navier Stokes Equations

This paper is concerned with the regularity criterion of weak solutions to the three-dimensional Navier-Stokes equations with nonlinear damping in critical weakLqspaces. It is proved that if the weak solution satisfies∫0T∇u1Lq,∞2q/2q-3+∇u2Lq,∞2q/2q-3/1+ln⁡e+∇uL22ds<∞,  q>3/2, then the weak solution of Navier-Stokes equations with nonlinear damping is regular on(0,T].

scholarly journals A Remark on the Regularity Criterion for the 3D Boussinesq Equations Involving the Pressure Gradient

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zujin Zhang
Keyword(s):  
Pressure Gradient ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

We consider the three-dimensional Boussinesq equations and obtain a regularity criterion involving the pressure gradient in the Morrey-Companato spaceMp,q. This extends and improves the result of Gala (Gala 2013) for the Navier-Stokes equations.

scholarly journals A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Stefano Bosia ◽  
Monica Conti ◽  
Vittorino Pata
Keyword(s):  
Pressure Gradient ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

AbstractThe incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.

scholarly journals A Regularity Criterion for Positive Part of Radial Component in the Case of Axially Symmetric Navier-Stokes Equations

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
Adam Kubica
Keyword(s):  
Stokes Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Radial Component ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Positive Part ◽  
Navier Stokes Equations ◽  
Three Dimensional Space

AbstractWe examine the conditional regularity of the solutions of Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of velocity satisfies a weighted Serrin type condition and in addition angular component satisfies some condition, then the solution is regular.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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