Long time existence of solutions to 2d Navier-Stokes equations with heat convection
Jolanta Socała ; Wojciech M. Zajączkowski
Applicationes Mathematicae, Tome 36 (2009), p. 453-463 / Harvested from The Polish Digital Mathematics Library
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Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that v,θ∈Ws2,1(ΩT), ∇p∈Ls(ΩT), s>2.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:279997 
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     title = {Long time existence of solutions to 2d Navier-Stokes equations with heat convection},
     journal = {Applicationes Mathematicae},
     volume = {36},
     year = {2009},
     pages = {453-463},
     zbl = {1179.35226},
     language = {en},
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Jolanta Socała; Wojciech M. Zajączkowski. Long time existence of solutions to 2d Navier-Stokes equations with heat convection. Applicationes Mathematicae, Tome 36 (2009) pp. 453-463. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-4-5/