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arXiv · 1808.06089

Energy equality in compressible fluids with physical boundaries

Robin Ming Chen·Zhilei Liang·Dehua Wang·Runzhang Xu
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Abstract

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.

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Robin Ming Chen, Zhilei Liang, Dehua Wang, Runzhang Xu. 2018-08-18. Energy equality in compressible fluids with physical boundaries. https://arxiv.org/abs/1808.06089

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