Geodesic
Concentrations problem for solutions to compressible Navier–Stokes equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 55-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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A three-dimensional initial-boundary value problem for the isentropic equations of the dynamics of a viscous gas is considered. The concentration phenomenon is that, for adiabatic exponent values $\gamma\le3/2$, the finite energy can be concentrated on arbitrarily small sets. It is proved that, in the critical case $\gamma=3/2$, the norm of the density of kinetic energy in the logarithmic Orlicz space is bounded by a constant that depends only on the initial and boundary data. This eliminates the possibility of the concentration phenomenon.
Keywords: Navier–Stokes equations, concentration phenomenon.
Mots-clés : viscous gas 
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     author = {P. I. Plotnikov},
     title = {Concentrations problem for solutions to compressible {Navier{\textendash}Stokes} equations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {55--58},
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     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_495_a11/}
}
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P. I. Plotnikov. Concentrations problem for solutions to compressible Navier–Stokes equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 55-58. http://geodesic.mathdoc.fr/item/DANMA_2020_495_a11/

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