Global well-posedness for an advection–diffusion equation arising in magneto-geostrophic dynamics
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, p. 283-301
We use De Giorgi techniques to prove Hölder continuity of weak solutions to a class of drift-diffusion equations, with L 2 initial data and divergence free drift velocity that lies in L t 𝐵𝑀𝑂 x -1 . We apply this result to prove global regularity for a family of active scalar equations which includes the advection–diffusion equation that has been proposed by Moffatt in the context of magnetostrophic turbulence in the Earthʼs fluid core.
Nous utilisons des techniques de De Giorgi pour démontrer la continuité Hölder de solutions faibles pour une classe dʼéquations de dérive-diffusion, avec données initiales L 2 et champ de vitesse incompressible appartenant à L t 𝐵𝑀𝑂 x -1 . Nous appliquons ce résultat pour démontrer la régularité globale pour une famille dʼéquations du scalaire actif qui comprend lʼéquation dʼadvection–diffusion qui a été proposée par Moffatt dans le contexte de la turbulence magnétostrophique dans le noyau fluide de la Terre.
DOI : https://doi.org/10.1016/j.anihpc.2011.01.002
Classification:  76D03,  35Q35,  76W05
Keywords: Global regularity, Weak solutions, De Giorgi, Parabolic equations, Magneto-geostrophic equations
@article{AIHPC_2011__28_2_283_0,
     author = {Friedlander, Susan and Vicol, Vlad},
     title = {Global well-posedness for an advection--diffusion equation arising in magneto-geostrophic dynamics},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {2},
     year = {2011},
     pages = {283-301},
     doi = {10.1016/j.anihpc.2011.01.002},
     zbl = {1277.35291},
     mrnumber = {2784072},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_2_283_0}
}
Friedlander, Susan; Vicol, Vlad. Global well-posedness for an advection–diffusion equation arising in magneto-geostrophic dynamics. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, pp. 283-301. doi : 10.1016/j.anihpc.2011.01.002. http://www.numdam.org/item/AIHPC_2011__28_2_283_0/

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