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- W2227187412 abstract "In a $d-$dimensional strip with $dgeq 2$, we study the non-stationary Stokes equation with no-slip boundary condition in the lower and upper plates and periodic boundary condition in the horizontal directions. In this paper we establish a new maximal regularity estimate in the real interpolation norm begin{equation*} ||f||_{(0,1)}=inf_{f=f_0+f_1}left{leftlanglesup_{0<z<1} |f_0|rightrangle+ leftlangleint_0^{1} |f_1| frac{dz}{(1-z)z}rightrangleright},, end{equation*} where the brackets $langlecdotrangle$ denotes the horizontal-space and time average. The norms involved in the definition of $|cdot|_{(0,1)}$ are critical for two reasons: the exponents are borderline for the Calder'on-Zygmund theory and the weight $1/z$ just fails to be Muckenhoupt. Therefore, the estimate is only true under horizontal bandedness condition, (i. e. a restriction to a packet of wave numbers in Fourier space). The motivation to express the maximal regularity in such a norm comes from an application to the Rayleigh-B'enard problem." @default.
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- W2227187412 date "2016-04-01" @default.
- W2227187412 modified "2023-10-17" @default.
- W2227187412 title "A maximal regularity estimate for the non-stationary Stokes equation in the strip" @default.
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- W2227187412 doi "https://doi.org/10.1016/j.jde.2015.12.010" @default.
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