Generalized function treatment of the Alfvén-gravity wave problem.
Geometry of fluid motion
We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [3].
Gli universi ipersferici, il gruppo conforme ed il campo gravitazionale di Newton.
Global existence and uniqueness of strong solutions for the magnetohydrodynamic equations.
Global existence of 2D slightly compressible viscous magneto-fluid motion.
Global existence of solutions for incompressible magnetohydrodynamic equations
Global-in-time existence of solutions for incompressible magnetohydrodynamic fluid equations in a bounded domain Ω ⊂ ℝ³ with the boundary slip conditions is proved. The proof is based on the potential method. The existence is proved in a class of functions such that the velocity and the magnetic field belong to and the pressure q satisfies for p ≥ 7/3.
Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid
Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible 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. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.
Global free boundary problem for incompressible magnetohydrodynamics [Book]
Global magnetofluidostatic fields (an unsolved PDE problem).
Global strong solutions of a 2-D new magnetohydrodynamic system
The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on --estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.
Global well-posedness for certain density-dependent modified-Leray- models.