A plane problem of incompressible magnetohydro-dynamics with viscosity and resistivity depending on the temperature

Giovanni Cimatti

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 2, page 137-146
  • ISSN: 1120-6330

Abstract

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The plane flow of a fluid obeying the equations of magnetohydrodynamics is studied under the assumption that both the viscosity and the resistivity depend on the temperature. Some results of existence, non-existence, and uniqueness of solution are proved.

How to cite

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Cimatti, Giovanni. "A plane problem of incompressible magnetohydro-dynamics with viscosity and resistivity depending on the temperature." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.2 (2004): 137-146. <http://eudml.org/doc/252386>.

@article{Cimatti2004,
abstract = {The plane flow of a fluid obeying the equations of magnetohydrodynamics is studied under the assumption that both the viscosity and the resistivity depend on the temperature. Some results of existence, non-existence, and uniqueness of solution are proved.},
author = {Cimatti, Giovanni},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Incompressible magnetohydrodynamics; Thermistor problem; Existence of solutions; incompressible magnetohydrodynamics; thermistor problem; existence of solutions},
language = {eng},
month = {6},
number = {2},
pages = {137-146},
publisher = {Accademia Nazionale dei Lincei},
title = {A plane problem of incompressible magnetohydro-dynamics with viscosity and resistivity depending on the temperature},
url = {http://eudml.org/doc/252386},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Cimatti, Giovanni
TI - A plane problem of incompressible magnetohydro-dynamics with viscosity and resistivity depending on the temperature
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/6//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 2
SP - 137
EP - 146
AB - The plane flow of a fluid obeying the equations of magnetohydrodynamics is studied under the assumption that both the viscosity and the resistivity depend on the temperature. Some results of existence, non-existence, and uniqueness of solution are proved.
LA - eng
KW - Incompressible magnetohydrodynamics; Thermistor problem; Existence of solutions; incompressible magnetohydrodynamics; thermistor problem; existence of solutions
UR - http://eudml.org/doc/252386
ER -

References

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  1. ALLEGRETTO, W. - XIE, H., A non-local thermistor problem. European J. of Appl. Math., v. 6, 1995, 83-94. Zbl0826.35120MR1317875DOI10.1017/S0956792500001686
  2. CIMATTI, G., Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions. Quart. Appl. Math., v. 97, 1989, 117-121. Zbl0694.35137MR987900
  3. CIMATTI, G. - PRODI, G., Existence results for a nonlinear elliptic system modelling a temperature dependent resistor. Ann. Math. Pura Appl., v. 62, 1988, 227-236. Zbl0675.35039MR980982DOI10.1007/BF01766151
  4. COWLING, T.G., Magnetohydrodynamics. InterscienceTracts on Physics, New York1957. Zbl0435.76086MR98556
  5. HOWISON, S.D., A note on the thermistor problem in two space dimensions. Quart. Appl. Math., v. 98, 1989, 37-39. Zbl0692.35094MR1012273
  6. LIONS, J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires. Etudes mathématiques, Dunod, Paris1969. Zbl0189.40603

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