American Institute of Mathematical Sciences

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2015, 2015(special): 349-358. doi: 10.3934/proc.2015.0349

Anisotropically diffused and damped Navier-Stokes equations

Hermenegildo Borges de Oliveira 1,

1. 

FCT - Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal

Received  September 2014 Revised  February 2015 Published  November 2015

The incompressible Navier-Stokes equations with anisotropic diffusion and anisotropic damping is considered in this work. For the associated initial-boundary value problem, we prove the existence of weak solutions and we establish an energy inequality satisfied by these solutions. We prove also under what conditions the solutions of this problem extinct in a finite time.
Keywords: extinction in a fi nite time., existence, anisotropic diff usion, Navier-Stokes, anisotropic damping.
Mathematics Subject Classification: Primary: 35Q35, 35D30, 35B40; Secondary: 76D05, 76D0.
Citation: Hermenegildo Borges de Oliveira. Anisotropically diffused and damped Navier-Stokes equations. Conference Publications, 2015, 2015 (special) : 349-358. doi: 10.3934/proc.2015.0349
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Adv. Math. Fluid Mech. Springer-Verlag (2010), 409-424. Google Scholar

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show all references

References:
[1]

Progr. Nonlinear Differential Equations Appl. 48, Birkhäuser, 2002. Google Scholar

[2]

Adv. Differential Equations 19 (2014) no. 5-6, 441-472. Google Scholar

[3]

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 1-26, First online: 17 December 2015. Google Scholar

[4]

Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004), no. 5, 715-734. Google Scholar

[5]

Appl. Anal. 93 (2014), no. 7, 1477-1494. Google Scholar

[6]

SIAM J. Math. Anal. 34 (2003), no. 5, 1064-1083. Google Scholar

[7]

Monatsh. Math. 158 (2009), no. 1, 71-79. Google Scholar

[8]

Commun. Pure Appl. Anal. 11 (2012), no. 5, 2037-2054. Google Scholar

[9]

Dunod, Paris, 1969. Google Scholar

[10]

Chapman & Hall, London, 1996. Google Scholar

[11]

Adv. Math. Fluid Mech. Springer-Verlag (2010), 409-424. Google Scholar

[12]

NoDEA Nonlinear Differential Equations Appl. 20 (2013) no. 3, 797-824. Google Scholar

[13]

Beiträge Anal. No. 15 (1980), 127-140 (1981). Google Scholar

[14]

Ricerche Mat. 18 (1969), 3-24. Google Scholar

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