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Remarks on Leray's self‐similar solutions to the 3D magnetohydrodynamic equations
Author(s) -
Benbernou Samia,
Ragusa Maria Alessandra,
Terbeche Mekki
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3001
Subject(s) - uniqueness , magnetohydrodynamic drive , mathematics , homogeneous , space (punctuation) , compressibility , function (biology) , mathematical analysis , function space , homogeneous function , magnetohydrodynamics , pure mathematics , mathematical physics , magnetic field , physics , combinatorics , thermodynamics , computer science , quantum mechanics , evolutionary biology , biology , operating system
In this note, we examine small self‐similar solutions of the 3D incompressible magnetohydrodynamic equations in homogenous function spaces and show the uniqueness of self‐similar solutions when the velocity field is small in some homogeneous function spaces. This extend the recent results given by C. He and Z. Xin. “On the self‐similar solutions of the magneto‐hydro‐dynamic equations. Acta Mathematica Scientia, série B English Edition 2009; 29 (3): 583–598”. It is a natural way to extend the space widely and improve the previous results. Copyright © 2013 John Wiley & Sons, Ltd.