TY - JOUR
T1 - Global small analytic solutions of MHD boundary layer equations
AU - Liu, Ning
AU - Zhang, Ping
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/4/25
Y1 - 2021/4/25
N2 - In this paper, we prove the global existence and the large time decay estimate of solutions to the two-dimensional MHD boundary layer equations with small initial data, which is analytical in the tangential variable. The main idea of the proof is motivated by that of [28]. The additional difficulties are: 1. There appears the magnetic field; 2. The far field here depends on the tangential variable; 3. The Reynolds number is different from magnetic Reynolds number. In particular, we solved an open question in [33] concerning the large time existence of analytical solutions to the MHD boundary layer equations.
AB - In this paper, we prove the global existence and the large time decay estimate of solutions to the two-dimensional MHD boundary layer equations with small initial data, which is analytical in the tangential variable. The main idea of the proof is motivated by that of [28]. The additional difficulties are: 1. There appears the magnetic field; 2. The far field here depends on the tangential variable; 3. The Reynolds number is different from magnetic Reynolds number. In particular, we solved an open question in [33] concerning the large time existence of analytical solutions to the MHD boundary layer equations.
KW - Analytic energy estimate
KW - Littlewood-Paley theory
KW - MHD Prandtl system
UR - http://www.scopus.com/inward/record.url?scp=85100608714&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2021.02.003
DO - 10.1016/j.jde.2021.02.003
M3 - Article
AN - SCOPUS:85100608714
SN - 0022-0396
VL - 281
SP - 199
EP - 257
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -