TY - JOUR
T1 - Periodic solution and asymptotic stability for the magnetohydrodynamic equations with inhomogeneous boundary condition
AU - Kondrashuk, Igor
AU - Notte-Cuello, Eduardo Alfonso
AU - Poblete-Cantellano, Mariano
AU - Rojas-Medar, Marko Antonio
N1 - Publisher Copyright:
© 2019 by the authors.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study the asymptotic stability for the time periodic solution for this system. In particular, when the magnetic field h(x, t) is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier-Stokes equations with inhomogeneous boundary conditions.
AB - We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study the asymptotic stability for the time periodic solution for this system. In particular, when the magnetic field h(x, t) is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier-Stokes equations with inhomogeneous boundary conditions.
KW - Magnetohydrodynamic equations
KW - Periodic solutions
UR - https://www.scopus.com/pages/publications/85066855122
U2 - 10.3390/axioms8020044
DO - 10.3390/axioms8020044
M3 - Article
AN - SCOPUS:85066855122
SN - 2075-1680
VL - 8
JO - Axioms
JF - Axioms
IS - 2
M1 - 44
ER -