Geodesic
Global strong solutions of a 2-D new magnetohydrodynamic system
Applications of Mathematics, Tome 65 (2020) no. 1, pp. 105-120 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg's estimates for the stationary Stokes equation and Solonnikov's theorem on $L^p$-$L^q$-estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.
The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg's estimates for the stationary Stokes equation and Solonnikov's theorem on $L^p$-$L^q$-estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.
DOI : 10.21136/AM.2020.0208-19
Classification : 35B65, 35D35, 35Q35, 35Q61, 76W05
Keywords: global strong solution; magnetohydrodynamics; Stokes equation; $L^p$-$L^q$-estimates 
@article{10_21136_AM_2020_0208_19,
     author = {Liu, Ruikuan and Yang, Jiayan},
     title = {Global strong solutions of a {2-D} new magnetohydrodynamic system},
     journal = {Applications of Mathematics},
     pages = {105--120},
     year = {2020},
     volume = {65},
     number = {1},
     doi = {10.21136/AM.2020.0208-19},
     mrnumber = {4064592},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0208-19/}
}
TY  - JOUR
AU  - Liu, Ruikuan
AU  - Yang, Jiayan
TI  - Global strong solutions of a 2-D new magnetohydrodynamic system
JO  - Applications of Mathematics
PY  - 2020
SP  - 105
EP  - 120
VL  - 65
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0208-19/
DO  - 10.21136/AM.2020.0208-19
LA  - en
ID  - 10_21136_AM_2020_0208_19
ER  - 
%0 Journal Article
%A Liu, Ruikuan
%A Yang, Jiayan
%T Global strong solutions of a 2-D new magnetohydrodynamic system
%J Applications of Mathematics
%D 2020
%P 105-120
%V 65
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0208-19/
%R 10.21136/AM.2020.0208-19
%G en
%F 10_21136_AM_2020_0208_19
Liu, Ruikuan; Yang, Jiayan. Global strong solutions of a 2-D new magnetohydrodynamic system. Applications of Mathematics, Tome 65 (2020) no. 1, pp. 105-120. doi: 10.21136/AM.2020.0208-19

Cité par Sources :