Abstract
It is well-known that a Leray-Hopf weak solution in L4(0,T;L4(T3)) for the incompressible Navier-Stokes system is persistence of energy due to Lions [19]. In this paper, it is shown that Lions's condition for energy balance is also valid for the weak solutions of the isentropic compressible Navier-Stokes equations allowing vacuum under suitable integrability conditions on the density and its derivative. This further allows us to establish various sufficient conditions implying energy equality for the compressible flow as well as the non-homogenous incompressible Navier-Stokes equations, which is an improvement of corresponding results obtained by Yu in [31, Arch. Ration. Mech. Anal., 225 (2017)] and answers a question posed by Liang in [18, Proc. R. Soc. Edinb., Sect. A, Math. (2020)].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
