Global small analytic solutions of MHD boundary layer equations

2020/06/22 by Liu, Ning, Zhang, Ping
#35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.11964

Abstract

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 \citePZ5. 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 \citeXY19 concerning the large time existence of analytical solutions to the MHD boundary layer equations.

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