Time-Periodic Weak Solutions to Incompressible Generalized Newtonian Fluids

AbstractIn this study we are interested in the Navier–Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of time-periodic three-dimensional flows.

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Weak Solutions and Their Kinetic Energy Regarding Time-Periodic Navier–Stokes Equations in Three Dimensional Whole-Space

Mathematics ◽

10.3390/math9131528 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1528

Author(s):

Mads Kyed

Keyword(s):

Kinetic Energy ◽

Weak Solutions ◽

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Periodic Forcing ◽

Navier Stokes Equations ◽

Whole Space ◽

Time Periodic Solutions ◽

Time Periodic

The existence of weak time-periodic solutions to Navier–Stokes equations in three dimensional whole-space with time-periodic forcing terms are established. The solutions are constructed in such a way that the structural properties of their kinetic energy are obtained. No restrictions on either the size or structure of the external force are required.

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Existence of time-periodic weak solutions to the stochastic Navier-Stokes equations around a moving body

Journal of Mathematical Physics ◽

10.1063/1.4850878 ◽

2013 ◽

Vol 54 (12) ◽

pp. 123101

Author(s):

Feng Chen ◽

Yuecai Han

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Moving Body ◽

Time Periodic ◽

Periodic Weak Solutions

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Time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space with a non-zero drift term: Asymptotic profile at spatial infinity

Mathematical Analysis in Fluid Mechanics - Contemporary Mathematics ◽

10.1090/conm/710/14367 ◽

2018 ◽

pp. 121-144

Author(s):

Giovanni Galdi ◽

Mads Kyed

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Spatial Infinity ◽

Navier Stokes Equations ◽

Drift Term ◽

Asymptotic Profile ◽

Whole Space ◽

Time Periodic Solutions ◽

Time Periodic

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The Kneser property of the weak solutions of the three dimensional Navier-Stokes equations

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2010.28.161 ◽

2010 ◽

Vol 28 (1) ◽

pp. 161-179 ◽

Cited By ~ 8

Author(s):

Peter E. Kloeden ◽

◽

José Valero ◽

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Navier Stokes Equations

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Existence of weak solutions to the three-dimensional steady compressible Navier–Stokes equations

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/j.anihpc.2011.02.008 ◽

2011 ◽

Vol 28 (4) ◽

pp. 485-498 ◽

Cited By ~ 27

Author(s):

Song Jiang ◽

Chunhui Zhou

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Existence Of Weak Solutions

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On the Existence of Periodic Weak Solutions on the Navier-Stokes Equations in Exterior Regions with Periodically Moving Boundaries

Navier—Stokes Equations and Related Nonlinear Problems ◽

10.1007/978-1-4899-1415-6_6 ◽

1995 ◽

pp. 63-73 ◽

Cited By ~ 8

Author(s):

Rodolfo Salvi

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Moving Boundaries ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Exterior Regions ◽

Periodic Weak Solutions

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Modelling of Laminar Canonical Flows: Revisit

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2012-72376 ◽

2012 ◽

Author(s):

Kofi Freeman K. Adane ◽

Mark F. Tachie

Keyword(s):

Three Dimensional ◽

Shear Thinning ◽

Secondary Flows ◽

Newtonian Fluids ◽

Navier Stokes ◽

Jet Flows ◽

Wall Jet ◽

Navier Stokes Equation ◽

Incompressible Navier Stokes Equation ◽

Insight Into

Three-dimensional laminar lid-driven and wall jet flows of various shear-thinning non-Newtonian and Newtonian fluids were numerically investigated. The complete nonlinear incompressible Navier-Stokes equation was solved using a collocated finite-volume based in-house CFD code. From the results, velocity profiles at several locations, jet spread rates, secondary flows and vorticity distributions were used to provide insight into the characteristics of three-dimensional laminar canonical flows of shear-thinning non-Newtonian and Newtonian fluids.

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Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system involving a tensor-valued sensitivity with saturation

Journal of Differential Equations ◽

10.1016/j.jde.2017.01.024 ◽

2017 ◽

Vol 262 (10) ◽

pp. 5271-5305 ◽

Cited By ~ 17

Author(s):

Ji Liu ◽

Yifu Wang

Keyword(s):

Weak Solutions ◽

Stokes System ◽

Three Dimensional ◽

Navier Stokes ◽

Global Weak Solutions

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Decay of weak solutions and the singular set of the three-dimensional Navier–Stokes equations

Nonlinearity ◽

10.1088/0951-7715/20/5/007 ◽

2007 ◽

Vol 20 (5) ◽

pp. 1185-1191 ◽

Cited By ~ 19

Author(s):

James C Robinson ◽

Witold Sadowski

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Singular Set ◽

Navier Stokes Equations

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Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

Advanced Nonlinear Studies ◽

10.1515/ans-2006-0304 ◽

2006 ◽

Vol 6 (3) ◽

Cited By ~ 27

Author(s):

Tomás Caraballo ◽

José Real ◽

Peter E. Kloeden

Keyword(s):

Weak Solutions ◽

Existence And Uniqueness ◽

Stokes Equations ◽

Three Dimensional ◽

Strong Solutions ◽

Navier Stokes ◽

Dimensional System ◽

Navier Stokes Equations ◽

Three Dimensional System

AbstractWe prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.

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