Regularity estimates for stationary Stokes problem in some generalized function spaces

We investigate the global regularity for weak solutions to a generalized stationary Stokes problem with BMO coefficients in a non-smooth domains. The results in this paper fall into two categories to get estimates for both velocity gradient and its associated pressure, corresponding to the two class...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2023-02, Vol.74 (1), Article 13
Main Authors: Nguyen, Thanh-Nhan, Tran, Minh-Phuong, Tran, N.-T.-Nhu
Format: Article
Language:English
Subjects:
Distribution functions
Engineering
Estimates
Function space
Mathematical Methods in Physics
Regularity
Theoretical and Applied Mechanics
Velocity gradient
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Summary:We investigate the global regularity for weak solutions to a generalized stationary Stokes problem with BMO coefficients in a non-smooth domains. The results in this paper fall into two categories to get estimates for both velocity gradient and its associated pressure, corresponding to the two classes of generalized function spaces. Our first outcome is the generalized Lorentz spaces Λ ν , ω s , t ( Ω ) estimate with Muckenhoupt weights. The second concerns a global bound in ψ -generalized Morrey spaces M s , ψ ( Ω ) . The proof technique in our study is an adaption of innovative method launched in Acerbi and Mingione (Duke Math J 136(2):285–320, 2007), and distinctive feature is that we employ the so-called fractional maximal distribution functions.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01901-x