On Lie reduction of MHD equations to partial differential equations with three independent variables. (English) Zbl 0912.35039
Samoilenko, A. M. (ed.) et al., Symmetric and analytic methods in mathematical physics. Series: Mathematical physics. Dedicated to the memory of V. I. Fushchich. Kyïv: Instytut Matematyky NAN Ukraïny. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 19, 177-185 (1998).
Equations of magnetohydrodynamics which describe flows of viscous homogeneous incompressible liquid of a finite electrical conductivity are under consideration. By using the Lie symmetry approach the initial system is reduced to a system of differential equations with partial derivatives with respect to three independent variables. Based on symmetry properties of the reduced system an algorithm for constructing of exact solutions to the initial problem is suggested.
For the entire collection see [Zbl 0902.00014].
For the entire collection see [Zbl 0902.00014].
Reviewer: Oleg Limarchenko (Kyïv)
MSC:
| 35C05 | Solutions to PDEs in closed form |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
