Global regularity of the incompressible magnetohydrodynamic equations on
3D thin domain with large data
Abstract
In this paper, we consider the incompressible magnetohydrodynamic
equations with Dirichlet boundary on a 3D thin domain Ω = ( 0 , l 1 ) ×
( 0 , l 2 ) × ( 0 , ε ) , where l 1 , l 2 > 0 , ε ∈ ( 0 , 1
) . We prove that if | | A 1 2 u 0 |
| L 2 + | | ∇ b 0 | | L 2 ≤
1 C ε 1 2 , then there exists a global smooth solution with the initial
data u 0 and b 0 .
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