September  2010, 26(3): 1019-1034. doi: 10.3934/dcds.2010.26.1019

Existence of solutions of the equations of electron magnetohydrodynamics in a bounded domain

1. 

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain

Received  June 2009 Revised  October 2009 Published  December 2009

Electron magnetohydrodynamics (EMHD) models the flow of electrons in fast time scales in an inhomogeneous plasma, by considering the ions as stationary. A number of numerical studies has shown an interesting phenomenology, but so far no proof exists of existence of solutions for the main equation. This equation is similar to the vorticity equation of inviscid flows, but the techniques used to prove local existence in that case do not work well in a bounded domain. However, the formulation of the Cauchy solution for certain transport equations plus a number of estimates on the Hölder norm of the flux of a vector field are enough to provide a proof of existence of solutions in a certain time interval.
Citation: Manuel Núñez. Existence of solutions of the equations of electron magnetohydrodynamics in a bounded domain. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1019-1034. doi: 10.3934/dcds.2010.26.1019
[1]

Rafael De La Llave, R. Obaya. Regularity of the composition operator in spaces of Hölder functions. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 157-184. doi: 10.3934/dcds.1999.5.157

[2]

Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692

[3]

Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467

[4]

Boris Muha. A note on the Trace Theorem for domains which are locally subgraph of a Hölder continuous function. Networks & Heterogeneous Media, 2014, 9 (1) : 191-196. doi: 10.3934/nhm.2014.9.191

[5]

Valerii Los, Vladimir A. Mikhailets, Aleksandr A. Murach. An isomorphism theorem for parabolic problems in Hörmander spaces and its applications. Communications on Pure & Applied Analysis, 2017, 16 (1) : 69-98. doi: 10.3934/cpaa.2017003

[6]

Charles Pugh, Michael Shub, Amie Wilkinson. Hölder foliations, revisited. Journal of Modern Dynamics, 2012, 6 (1) : 79-120. doi: 10.3934/jmd.2012.6.79

[7]

Jinpeng An. Hölder stability of diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 315-329. doi: 10.3934/dcds.2009.24.315

[8]

Angelo Favini, Rabah Labbas, Stéphane Maingot, Hiroki Tanabe, Atsushi Yagi. Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 973-987. doi: 10.3934/dcds.2008.22.973

[9]

Wenning Wei. On the Cauchy-Dirichlet problem in a half space for backward SPDEs in weighted Hölder spaces. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5353-5378. doi: 10.3934/dcds.2015.35.5353

[10]

Jeffrey W. Lyons. An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem. Conference Publications, 2015, 2015 (special) : 775-782. doi: 10.3934/proc.2015.0775

[11]

Sergey P. Degtyarev. On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions. Evolution Equations & Control Theory, 2015, 4 (4) : 391-429. doi: 10.3934/eect.2015.4.391

[12]

Nicholas Long. Fixed point shifts of inert involutions. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297

[13]

Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557

[14]

Luis Barreira, Claudia Valls. Hölder Grobman-Hartman linearization. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 187-197. doi: 10.3934/dcds.2007.18.187

[15]

Luca Lorenzi. Optimal Hölder regularity for nonautonomous Kolmogorov equations. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 169-191. doi: 10.3934/dcdss.2011.4.169

[16]

Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19

[17]

Andrey Kochergin. A Besicovitch cylindrical transformation with Hölder function. Electronic Research Announcements, 2015, 22: 87-91. doi: 10.3934/era.2015.22.87

[18]

Walter Allegretto, Yanping Lin, Shuqing Ma. Hölder continuous solutions of an obstacle thermistor problem. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 983-997. doi: 10.3934/dcdsb.2004.4.983

[19]

Slobodan N. Simić. Hölder forms and integrability of invariant distributions. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 669-685. doi: 10.3934/dcds.2009.25.669

[20]

Pedro Duarte, Silvius Klein, Manuel Santos. A random cocycle with non Hölder Lyapunov exponent. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4841-4861. doi: 10.3934/dcds.2019197

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]