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Volume 24, Issue 4
On the Steady Solutions to a Model of Compressible Heat Conducting Fluid in Two Space Dimensions

Milan Pokorný

DOI: 10.4208/jpde.v24.n4.5

J. Part. Diff. Eq., 24 (2011), pp. 334-350.

Published online: 2011-11

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  • Abstract

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain with the pressure law p(\varrho,ϑ)∼\varrhoϑ+\varrho ln^α(1+\varrho). For the heat flux q∼-(1+ϑ^m)∇ϑ we show the existence of a weak solution provided α > max{1,1/m}, m > 0. This improves the recent result from [1].

  • Keywords

Steady compressible Navier-Stokes-Fourier system weak solution entropy inequality Orlicz spaces compensated compactness renormalized solution

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COPYRIGHT: © Global Science Press

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@Article{JPDE-24-334, author = {Milan Pokorný }, title = {On the Steady Solutions to a Model of Compressible Heat Conducting Fluid in Two Space Dimensions}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {4}, pages = {334--350}, abstract = {

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain with the pressure law p(\varrho,ϑ)∼\varrhoϑ+\varrho ln^α(1+\varrho). For the heat flux q∼-(1+ϑ^m)∇ϑ we show the existence of a weak solution provided α > max{1,1/m}, m > 0. This improves the recent result from [1].

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n4.5}, url = {http://global-sci.org/intro/article_detail/jpde/5215.html} }
TY - JOUR T1 - On the Steady Solutions to a Model of Compressible Heat Conducting Fluid in Two Space Dimensions AU - Milan Pokorný JO - Journal of Partial Differential Equations VL - 4 SP - 334 EP - 350 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.5 UR - https://global-sci.org/intro/article_detail/jpde/5215.html KW - Steady compressible Navier-Stokes-Fourier system KW - weak solution KW - entropy inequality KW - Orlicz spaces KW - compensated compactness KW - renormalized solution AB -

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain with the pressure law p(\varrho,ϑ)∼\varrhoϑ+\varrho ln^α(1+\varrho). For the heat flux q∼-(1+ϑ^m)∇ϑ we show the existence of a weak solution provided α > max{1,1/m}, m > 0. This improves the recent result from [1].

Milan Pokorný . (2011). On the Steady Solutions to a Model of Compressible Heat Conducting Fluid in Two Space Dimensions. Journal of Partial Differential Equations. 24 (4). 334-350. doi:10.4208/jpde.v24.n4.5
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