Variational and operator methods for Maxwell-Stokes system
DOI10.3934/dcds.2020036zbMath1435.35368OpenAlexW2980454810MaRDI QIDQ2309173
Publication date: 30 March 2020
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2020036
Maxwell equationsvariational methodreduction methoddomain topologycurl equationMaxwell-Stokes systemmodified de Rham lemmamagneto-static problem
Variational methods involving nonlinear operators (47J30) PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) Variational methods applied to PDEs (35A15) Stokes and related (Oseen, etc.) flows (76D07) Variational methods for elliptic systems (35J50) de Rham theory in global analysis (58A12) Variational methods for second-order elliptic equations (35J20) Electro- and magnetostatics (78A30) Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47) Quasilinear elliptic equations (35J62) Quasilinear parabolic equations (35K59) Boundary value problems for second-order elliptic systems (35J57) Model reduction in optics and electromagnetic theory (78M34)
Related Items (7)
Cites Work
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- On the shape of meissner solutions to a limiting form of Ginzburg-Landau systems
- Ground states of time-harmonic semilinear Maxwell equations in \(\mathbb R^3\) with vanishing permittivity
- Existence and regularity of solutions to quasilinear systems of Maxwell type and Maxwell-Stokes type
- Cylindrically symmetric ground state solutions for curl-curl equations with critical exponent
- On a quasilinear system involving the operator curl
- Éléments finis mixtes incompressibles pour l'équation de Stokes dans \(R^ 3\).
- On the existence and regularity of the solution of Stokes problem in arbitrary dimension
- A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric
- Landau-de Gennes model of liquid crystals and critical wave number
- Meissner states of type II superconductors
- Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
- Towards a unified field theory for classical electrodynamics
- On generalized harmonic fields in domains with anisotropic nonhomogeneous media
- Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields
- On traces for \(\mathbf H(\text{curl},\Omega)\) in Lipschitz domains.
- Quasilinear elliptic system arising in a three-dimensional type-II superconductor for infinite \(\kappa\)
- Weak solution theory for Maxwell's equations in the semistatic limit case
- Hodge decomposition. A method for solving boundary value problems
- Singularities of electromagnetic fields in polyhedral domains
- Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
- Dual variational methods in critical point theory and applications
- Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems
- Nucleation of instability of the Meissner state of 3-dimensional superconductors
- Numerical analysis of nonlinear multiharmonic eddy current problems
- Su un problema al contorno relativo al sistema di equazioni di Stokes
- Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds
- Asymptotics of minimizers of variational problems involving curl functional
- Ground state solutions for semilinear time-harmonic Maxwell equations
- Functionals with Operator Curl in an Extended Magnetostatic Born--Infeld Model
- Radially symmetric solutions for a limiting form of the Ginzburg—Landau model
- On a quasilinear system arising in the theory of superconductivity
- An Introduction to the Mathematical Theory of the Navier-Stokes Equations
- An Efficient Eddy Current Model for Nonlinear Maxwell Equations with Laminated Conductors
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
- Significance of Electromagnetic Potentials in the Quantum Theory
- $L^r$-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains
- A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
- Minimizing curl in a multiconnected domain
- On the boundary value problems of electro- and magnetostatics
- Finite Element Methods for Navier-Stokes Equations
- Estimating ∇u by divu and curlu
- Vector potentials in three-dimensional non-smooth domains
- Schauder estimates for boundary layer potentials
- A remark on the characterization of the gradient of a distribution
- Quasilinear systems involving curl
- A Variational Problem Related to Self-trapping of an Electromagnetic Field
- Superheating Field of Type II Superconductors
- Lp-THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS
- Oblique Derivative Problems for Elliptic Equations
- An extended magnetostatic Born-Infeld model with a concave lower order term
- Regularity of weak solutions to nonlinear Maxwell systems
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