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Evolution of current sheets and regularity of ideal incompressible magnetic fluids in 2D
Author(s) -
Cordoba Diego,
Marliani Christiane
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200004)53:4<512::aid-cpa4>3.0.co;2-r
Subject(s) - mathematics , compressibility , singularity , magnetohydrodynamic drive , saddle , bounded function , ideal (ethics) , stream function , magnetohydrodynamics , mathematical analysis , exponential function , function (biology) , focus (optics) , geometry , mechanics , magnetic field , physics , mathematical optimization , law , vortex , vorticity , optics , quantum mechanics , evolutionary biology , political science , biology
The ideal incompressible magnetohydrodynamic equations in two dimensions are studied analytically and numerically. We focus on a standard scenario of singularity formation where level sets of the magnetic stream function contain a hyperbolic saddle. Analytically we obtain an exponential estimate on the closing of the angle under the assumption that the velocity remains bounded. This result is supported by high‐resolution numerical simulations using adaptive structured mesh refinement. © 2000 John Wiley & Sons, Inc.