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Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic compressible fluid

Piotr Kacprzyk (2004)

Applicationes Mathematicae

Local existence of solutions for the equations describing the motion of a magnetohydrodynamic compressible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linearized equations is proved, next by the method of successive aproximations local existence to the nonlinear problem is shown....

Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid

Piotr Kacprzyk (2003)

Applicationes Mathematicae

Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linarized equations is proved; next by the method of successive aproximations the local existence is shown for the nonlinear problem....

Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods

Basil Nicolaenko, Alex Mahalov, Timofey Shilkin (2006/2007)

Séminaire Équations aux dérivées partielles

We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space L 3 ( R 3 ) . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally L 3 . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.

Local-in-time existence for the non-resistive incompressible magneto-micropolar fluids

Peixin Zhang, Mingxuan Zhu (2022)

Applications of Mathematics

We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data u 0 ∈ H s - 1 + ε , w 0 ∈ H s - 1 and b 0 ∈ H s for s > 3 2 and any 0 < ε < 1 . The initial regularity of the micro-rotational velocity w is weaker than velocity of the fluid u .

Long-time stability of noncharacteristic viscous boundary layers

Toan Nguyen, Kevin Zumbrun (2009/2010)

Séminaire Équations aux dérivées partielles

We report our results on long-time stability of multi–dimensional noncharacteristic boundary layers of a class of hyperbolic–parabolic systems including the compressible Navier–Stokes equations with inflow [outflow] boundary conditions, under the assumption of strong spectral, or uniform Evans, stability. Evans stability has been verified for small-amplitude layers by Guès, Métivier, Williams, and Zumbrun. For large–amplitudes, it may be checked numerically, as done in one–dimensional case for isentropic...

Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

Erwan Deriaz, Bruno Despres, Gloria Faccanoni, Kirill Pichon Gostaf, Lise-Marie Imbert-Gérard, Georges Sadaka, Remy Sart (2011)

ESAIM: Proceedings

FreeFem++ [11] is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma...

Magneto-micropolar fluid motion: existence of weak solutions.

Marko A. Rojas-Medar, José Luiz Boldrini (1998)

Revista Matemática Complutense

By using the Galerkin method, we prove the existence of weak solutions for the equations of the magneto-micropolar fluid motion in two and three dimensions in space. In the two-dimensional case, we also prove that such weak solution is unique. We also prove the reproductive property.

Modeling, mathematical and numerical analysis of electrorheological fluids

Michael Růžička (2004)

Applications of Mathematics

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.

Currently displaying 81 – 100 of 222