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Blow‐up of the maximal solution to 3D Boussinesq system in Lei‐Lin‐Gevrey spaces
Author(s) -
Selmi Ridha,
Chaabani Abdelkerim,
Zaabi Mounia
Publication year - 2020
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.6091
Subject(s) - mathematics , interpolation (computer graphics) , mathematical analysis , decomposition , function (biology) , pure mathematics , classical mechanics , physics , ecology , evolutionary biology , biology , motion (physics)
For arbitrary initial data in Lei‐Lin‐Gevrey spaces, we investigate the blow‐up phenomena in finite time to the local unique solution of the three‐dimensional Boussinesq system. We determine the blow‐up profile explicitly as a function of time, and we identify the low frequencies part as a solely responsible of this phenomena. Frequencies decomposition, functional spaces interpolation, and Leray theory are used.