Small Alfvén number limit for incompressible magneto-hydrodynamics in a domain with boundaries
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for any fixed Alfvén number, the local well-posedness is proved for the equations of three-dimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth solution is shown to exist in a time interval independent of the Alfvén number, and the solutions of the original system tend to the solutions of a two-dimensional Euler flow coupled with a linear transport equation as the Alfvén number goes to zero.
KeywordsMHD equations vanishing Alfvén number limit small Mach number uniform estimates
This work was supported by the Israel Science Foundation-National Natural Science Foundation of China Joint Research Program (Grant No. 11761141008). The first author was supported by the National Basic Research Program of China (Grant No. 2014CB745002) and National Natural Science Foundation of China (Grant No. 11631008). The second author was supported by National Natural Science Foundation of China (Grant Nos. 11571046, 11471028 and 11671225) and Beijing Natural Science Foundation (Grant No. 1182004). The authors thank Professor Steve Schochet from Tel-Aviv University for helpful discussions.
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