Abstract
Jour.Diff.Eq. 260 (2016) 5589-5626 In ad- dimensional strip withd≥ 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 equation* ||f||₍0,1)=ınf_(f)=f₀+f₁_0<z<1 |f₀|+ ınt₀¹ |f₁| dz(1-z)z
,, equation* where the brackets〈⋅〉denotes the horizontal-space and time average. The norms involved in the definition of‖⋅‖_((0,1))are critical for two reasons: the exponents are borderline for the Calderón-Zygmund theory and the weight1/zjust 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-Bénard problem.