Non-uniform dependence on initial data for the 2D MHD-Boussinesq equations

Non-uniform dependence on initial data for the 2D MHD-Boussinesq equations

In this paper, we will give the first result concerning the non-uniform dependence on initial data for the 2D magnetohydrodynamics (MHD)-Boussinesq equations as a hyperbolic-parabolic system. More precisely, we prove that the data-to-solution map of the Cauchy problem to the 2D MHD-Boussinesq equati...

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Veröffentlicht in:Journal of mathematical physics 2021-12, Vol.62 (12)
Hauptverfasser: Yu, Yanghai, Yang, Xiaolei
Format: Artikel
Sprache:eng
Schlagworte:
Boussinesq equations
Cauchy problems
Magnetohydrodynamics
Mathematical analysis
Physics
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Zusammenfassung:In this paper, we will give the first result concerning the non-uniform dependence on initial data for the 2D magnetohydrodynamics (MHD)-Boussinesq equations as a hyperbolic-parabolic system. More precisely, we prove that the data-to-solution map of the Cauchy problem to the 2D MHD-Boussinesq equations is not uniformly continuous in Hs with s > 2.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0060974