WebAug 31, 2024 · 1. 2. In this paper, we study the energy equality for weak solutions to the 3D homogeneous incompressible magnetohydrodynamic equations with viscosity and magnetic diffusion in a bounded domain. Two types of regularity conditions are imposed on weak solutions to ensure the energy equality. For the first type, some global integrability … WebIn this note, we prove that the weak solution (u ,B ) of the MHD system satisfies the energy equality, provided that one of the following assumptions is satisfied: (i) u ,B ∈Lq(0 ,T ;Lp(Ω …
On the energy equality for very weak solutions to 3D MHD
It is reasonable to conjecture that the energy equality of MHD system may hold under other assumptions only on the velocity fields, since [12] showed regularity criteria with assumptions only on \mathbf {u}. Observations of space and laboratory plasmas [11] also support the opinion that an incompressible three … See more Let \mathbf {f},\mathbf {g}\in L^2(0,T;L^2(\Omega )) and (\mathbf {u},\mathbf {B})\in L^2(0,T;H_0^1(\mathrm{div}\,0,\Omega ))\times … See more ([27, Lemma 3.1]) Suppose that (\mathbf {u}(t),\mathbf {B}(t)) is a weak solution to MHD on time interval [0, T] with 0 WebThe liquid-metal magnetohydrodynamic (MHD) powerplant is a nonrotating system usable with liquid-metal cooled reactors. In this system, a liquid metal is accelerated by vapor in … greater anglia rail cards
(PDF) A regularity criterion of the 3D MHD equations involving one ...
WebThe paper concentrates particularly on sources of fixed frequency, and solutions satisfying the radiation condition; but an Appendix is devoted to waves generated by a source of finite duration in an initially quiescent medium, and to unstable systems. WebJun 1, 2024 · 1. Introduction. Magnetohydrodynamicpower (MHD) generation is based on Faraday’s law of electromagnetic induction, with the working fluid in this device being a … WebMHD can be described by a set of equations consisting of a continuity equation, an equation of motion, an equation of state, Ampère's Law, Faraday's law, and Ohm's law. As with any … flight vocabulary grade 6