Energy conservation for the nonhomogeneous incompressible ideal Hall-MHD equations. (English) Zbl 1461.76555
Summary: In this paper, we study the energy conservation for the nonhomogeneous incompressible ideal Hall-magnetohydrodynamic system. Three types of sufficient conditions are obtained. Precisely, the first one provides \(\rho , u, P\), and \(b\) with sufficient regularity to ensure the local energy conservation. The second one removes the regularity condition on \(P\) while requires \(L^p\) regularity on the spatial gradient of the density \(\nabla \rho\) and \(L^r\) regularity on \(\rho_t\). The last one removes the regularity condition on \(\rho_t\) while requires certain time regularity on the velocity field \(u\). Our main strategy relies on commutator estimates in the work of P. Constantin et al. [Commun. Math. Phys. 165, No. 1, 207–209 (1994; Zbl 0818.35085)].
©2021 American Institute of Physics
©2021 American Institute of Physics
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 35Q35 | PDEs in connection with fluid mechanics |
Citations:
Zbl 0818.35085References:
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