Energy equality in compressible fluids with physical boundaries

We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an \(L^p\)-\(L^q\) regularity conditions on the velocity field for the energy equality to hold, provided that the density is bounded and satisfies \(\sqrt{\...

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Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Chen, Robin Ming, Liang, Zhilei, Wang, Dehua, Xu, Runzhang
Format: Article
Language:English
Subjects:
Compressible fluids
Fluid dynamics
Velocity distribution
Online Access:Get full text
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Summary:We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an \(L^p\)-\(L^q\) regularity conditions on the velocity field for the energy equality to hold, provided that the density is bounded and satisfies \(\sqrt{\rho} \in L^\infty_t H^1_x\). The main idea is to construct a global mollification combined with an independent boundary cut-off, and then take a double limit to prove the convergence of the resolved energy.
ISSN:2331-8422