Shear flow past a flat plate in hydromagnetics.
Shear layer solutions of incompressible MHD and dynamo effect
Singularity methods for magnetohydrodynamics.
Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem
This paper deals with a system of equations describing the motion of viscous electrically conducting incompressible fluid in a bounded three dimensional domain whose boundary is perfectly conducting. The displacement current appearing in Maxwell’s equations, is not neglected. It is proved that for a small periodic force and small positive there exists a locally unique periodic solution of the investigated system. For , these solutions are shown to convergeto a solution of the simplified (and...
Solution of a nonstationary boundary value problem for internal magnetohydrodynamics waves on the interface of layers of a conducting fluid.
Solution of the system of differential equations related to Marangoni convections in one fluid layer.
Solvability of control problems for stationary equations of magnetohydrodynamics of a viscous fluid.
Some geometric properties of magneto-fluid flows.
Some new parallel flows in weakly conducting fluids with an exponentially decaying Lorentz force.
Some results regarding the ultrasonic cavitation.
Some special solutions of self similar type in MHD, obtained by a separation method of variables
Some special solutions of self similar type in MHD, obtained by a separation method of variables
We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables Φ1, Φ2, Φ3 in addition to the time variable t and then in searching a solution which is separated with respect to Φ1 and t only. This is allowed by a very simple relation, called a “metric separation equation”, which governs the type of solutions with respect to time. The families...
Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai
The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information...
Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field.
Stabilized Galerkin methods for magnetic advection
Taking the cue from stabilized Galerkin methods for scalar advection problems, we adapt the technique to boundary value problems modeling the advection of magnetic fields. We provide rigorous a priori error estimates for both fully discontinuous piecewise polynomial trial functions and -conforming finite elements.
Stable discretization of a diffuse interface model for liquid-vapor flows with surface tension
The isothermal Navier–Stokes–Korteweg system is used to model dynamics of a compressible fluid exhibiting phase transitions between a liquid and a vapor phase in the presence of capillarity effects close to phase boundaries. Standard numerical discretizations are known to violate discrete versions of inherent energy inequalities, thus leading to spurious dynamics of computed solutions close to static equilibria (e.g., parasitic currents). In this work, we propose a time-implicit discretization of...
Stable upwind schemes for the magnetic induction equation
We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is shown to be...
Structure of the set of stationary solutions of viscous hydromagnetic equations with diffusivity
Study of Anisotropic MHD system in Anisotropic Sobolev spaces
Three-dimensional anisotropic magneto-hydrodynamical system is investigated in the whole space . Existence and uniqueness results are proved in the anisotropic Sobolev space for . Asymptotic behavior of the solution when the Rossby number goes to zero is studied. The proofs, where the incompressibility condition is crucial, use the energy method, an appropriate dyadic decomposition of the frequency space, product laws in anisotropic Sobolev spaces and Strichartz-type estimates.
Su alcuni casi limiti della magnetoidrodinamica.