Thank you for reading electrodynamics of continuous media. Maybe you have knowledge that, people have look numerous times for their chosen books like this electrodynamics of continuous media, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they cope with some malicious bugs inside their computer. electrodynamics of continuous media is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the electrodynamics of continuous media is universally compatible with any devices to read.

Electrodynamics Of Continuous Media

The goal of this final chapter is to show how the boundary value problems of mathematical physics can be solved by the methods of the preceding chapters. This will be done by solving a variety of specific problems that illustrate the principal types of problems that were formulated in Chapter 7. Additional applications are developed in the Exercises. The primary solution method is Fourier’s method of separation of variables and the associated Sturm-Liouville theory of Chapter 8.

Boundary Value Problems of Mathematical Physics

Studies in Advanced Mathematics

We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider turn out to be only of 
 $$C^{3/2+\epsilon }$$
 -class for some $$\epsilon >0$$
 and consequently have unbounded curvature, while the initial velocities are only Lipschitz. We reduce the system using a paradifferential approach.

On the Cauchy problem for gravity water waves

Pseudo-differential and Fourier series operators on the torus ${{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}$
 
are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is established. Periodization of operators and hyperbolic partial differential equations is discussed. Fourier series operators, which are analogues of Fourier integral operators on the torus, are introduced, and formulae for their compositions with pseudo-differential operators are derived. It is shown that pseudo-differential and Fourier series operators are bounded on L
 2 under certain conditions on their phases and amplitudes.

https://biblio.ugent.be/publication/8585517/file/8585518.pdf

Quantization of Pseudo-differential Operators on the Torus

We consider the free boundary problem for the plasma vacuum interface model in ideal incompressible magneto-hydrodynamics. Under a suitable stability condition on the initial discontinuity, the well-posedness of the linearized problem, around a non constant basic state sufficiently smooth, is investigated. Since the latter amounts to be a non standard initial-boundary value problem of mixed hyperbolic-elliptic type, for its resolution we introduce a fully ”hyperbolic” regularized problem. For the regularized problem, a suitable a priori estimate, uniform with respect to the small parameter of the regularization, is derived in the anisotropic Sobolev space H 1 .

/pdf/well-posedness-of-the-linearized-plasma-vacuum-interface-58o9hggqh8.pdf

Well-posedness of the linearized plasma-vacuum interface problem in ideal incompressible MHD

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics.

https://hal.archives-ouvertes.fr/hal-00565759/document

A priori Estimates for 3D Incompressible Current-Vortex Sheets

https://alessandro-morando.unibs.it/Slides/slides-files/praga08.pdf

Stability of incompressible current-vortex sheets

We consider the initial-boundary value problem for linear Friedrichs symmetrizable systems with characteristic boundary of constant rank. We assume the existence of the strong L2 solution satisfying a suitable energy estimate, but we do not assume any structural assumption sufficient for existence, such as the fact that the boundary conditions are maximally dissipative or the Kreiss–Lopatinski condition. We show that this is enough in order to get the regularity of solutions, in the natural framework of weighted anisotropic Sobolev spaces, provided the data are sufficiently smooth.

/pdf/regularity-of-solutions-to-characteristic-initial-boundary-33ly1s35yu.pdf

Regularity of solutions to characteristic initial-boundary value problems for symmetrizable systems

Using a classical result of Marcinkiewicz and Lizorkin about the L
 p
 -continuity for Fourier multipliers, the authors study the action of a class of pseudodifferential operators with weighted smooth symbol on a family of weighted Sobolev spaces. Results about L
 p
 -regularity for multi-quasi-elliptic pseudodifferential operators are also given.

Alessandro Morando

Papers

Well-posedness of the linearized plasma-vacuum interface problem in ideal incompressible MHD

A priori Estimates for 3D Incompressible Current-Vortex Sheets

Stability of incompressible current-vortex sheets

Regularity of solutions to characteristic initial-boundary value problems for symmetrizable systems

Lp-Bounded Pseudodifferential Operators and Regularity for Multi-quasi-elliptic Equations