Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 191-204 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe asymptotic solutions of the Cauchy problem for a linearized system of magnetohydrodynamics with initial conditions localized in a small neighborhood of a curve or a two-dimensional surface. We investigate how a change of the multiplicity of characteristics affects such solutions and prove a uniform estimate of the residual.
Mots-clés : magnetohydrodynamic equation
Keywords: nonstandard characteristic.
@article{TMF_2017_190_1_a13,
     author = {A. I. Allilueva and A. I. Shafarevich},
     title = {Nonstandard characteristics and localized asymptotic solutions of a~linearized magnetohydrodynamic system with small viscosity and drag},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {191--204},
     year = {2017},
     volume = {190},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a13/}
}
TY  - JOUR
AU  - A. I. Allilueva
AU  - A. I. Shafarevich
TI  - Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 191
EP  - 204
VL  - 190
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a13/
LA  - ru
ID  - TMF_2017_190_1_a13
ER  - 
%0 Journal Article
%A A. I. Allilueva
%A A. I. Shafarevich
%T Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 191-204
%V 190
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a13/
%G ru
%F TMF_2017_190_1_a13
A. I. Allilueva; A. I. Shafarevich. Nonstandard characteristics and localized asymptotic solutions of a linearized magnetohydrodynamic system with small viscosity and drag. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 191-204. http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a13/

[1] H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluid, Cambridge Univ. Press, Cambridge, 1978

[2] S. Friedlander, M. M. Vishik, “On stability and instability criteria for magnetohydrodynamics”, Chaos, 5:2 (1995), 416–423 | DOI | MR | Zbl

[3] V. V. Kucherenko, “Waves in the linearized system of magnetohydrodynamics”, Russ. J. Math. Phys., 17:3 (2010), 272–279 | DOI | MR | Zbl

[4] V. V. Kucherenko, A. Kryvko, “Interaction of Alfven waves in the linearized system of magnetohydrodynamics for an incompressible ideal fluid”, Russ. J. Math. Phys., 20:1 (2013), 56–67 | DOI | MR | Zbl

[5] V. P. Maslov, Operatornye metody, Nauka, M., 1973 | MR | Zbl

[6] A. Fridman, Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968 | MR | Zbl | Zbl

[7] A. I. Shafarevich, “Povedenie magnitnogo polya v provodyaschei zhidkosti s bystromenyayuschimsya polem skorostei”, Dokl. RAN, 360:1 (1998), 31–33 | MR | Zbl

[8] A. I. Esina, A. I. Shafarevich, “Delta-type solutions for a system of induction equations with discontinuous velocity field”, Methods Funct. Anal. Topology, 20:1 (2014), 17–33 | MR | Zbl