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arXiv · 1906.07478

Refined blow up criteria for the full compressible Navier-Stokes equations involving temperature

Quansen Jiu·Yanqing Wang·Yulin Ye
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Abstract

In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier-Stokes equations, we improve almost all the blow up criteria involving temperature to allow the temperature in its scaling invariant space for the 3D full compressible Navier-Stokes equations. Enlightening regular criteria via pressure $\Pi=\frac{\text {divdiv}}{-\Delta}(u_{i}u_{j})$ of the 3D incompressible Navier-Stokes equations on bounded domain, we generalize Beirao da Veiga's result in [1] from the incompressible Navier-Stokes equations to the isentropic compressible Navier-Stokes system in the case away from vacuum.

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Quansen Jiu, Yanqing Wang, Yulin Ye. 2019-06-18. Refined blow up criteria for the full compressible Navier-Stokes equations involving temperature. https://doi.org/10.1063/5.0024184

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