Magnetohydrodynamics

2D MHD — velocity + magnetic field coupling, Alfvén waves

∂ᵥ/∂t = −(v·∇)v + (J×B)/ρ + ν∇²v | ∂B/∂t = ∇×(v×B) + η∇²B | J = ∇×B | Alfvén speed: v_A = B/√(μ₀ρ)