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An Osgood type regularity criterion for the 2D Oldroyd‐B model
Author(s) -
Chen Qionglei,
Hao Xiaonan
Publication year - 2019
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.5464
Subject(s) - mathematics , type (biology) , compressibility , operator (biology) , curl (programming language) , pure mathematics , mathematical analysis , spectrum (functional analysis) , fourier transform , physics , ecology , biology , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor , computer science , programming language , thermodynamics
By means of the Littlewood‐Paley decomposition and the div‐curl Theorem by Coifman‐Lions‐Meyer‐Semmes, we prove an Osgood type regularity criterion for the 2D incompressible Oldroyd‐B model, that is,sup 2 ≤ N < + ∞∫ 0 T∑ | j | ≤ N ‖Δ ˙ j τ ‖ L ∞N log N d s , whereΔ ˙ j denotes the Fourier localization operator whose spectrum is supported in the shell {| ξ |≈2 j }.
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