| The first part of this paper focuses on the energy equality for weak solutions of the incompressible Hall-magnetohydrodynamics equations in a bounded domain Ω?Rn(n≥2),the model is described:By using the commutator estimates to deal with the nonlinear term and the coarea formula to treat the boundary term,we obtain several sufficient conditions to ensure that the energy equality is valid.For the special case n=3,p=q=2,our results are consistent with the corresponding results obtained by Kang-Deng-Zhou in[Results Appl.Math.12:100178,2021].Additionally,we establish the sufficient conditions concerning ▽u and ▽b,instead of u and b.In the second part,we mainly study the energy equality for weak solutions of the compressible Navier-Stokes-Korteweg equations in a bounded domain Ω? Rn(n=2,3),the model is as follows:By exploiting the coarea formula to treat the boundary term and the commutator estimates to deal with the nonlinear term,we obtain the sufficient conditions to ensure that energy equality holds. |
