Abstract Let Ω⊂ R d be a bounded open connected set with Lipschitz boundary. Let AN and
AD be the Stokes Neumann operator and Stokes Dirichlet operator on Ω, respectively. We …

Originally conceived to be the final volume of a trilogy on Analysis in Banach spaces,
containing the applications of the infrastructure of Volumes I–II to Harmonic and Stochastic …

We establish resolvent estimates in L q spaces for the Stokes operator in a bounded C 1
domain Ω in R d. As a corollary, it follows that the Stokes operator generates a bounded …

We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid
body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the …

We establish a local-in-space short-time smoothing effect for the Navier-Stokes equations in
the half space. The whole space analogue, due to Jia and Šverák [21], is a central tool in two …

This paper studies the Neumann boundary value problems for the Stokes equations in a
convex domain in $\mathbb {R}^ d $. We obtain nontangential-maximal-function estimates in …

The aim of this article is to deepen the understanding of the derivation of L^ p L p-estimates
of non-local operators. We review the L^ p L p-extrapolation theorem of Shen (2005) which …

We establish functional analytic properties of the Stokes operator with bounded measurable
coefficients on $ L^ p_ {\sigma}(\mathbb {R}^ d) $, $ d\geq 2$, for $\lvert 1/p-1/2\rvert< 1/d …

This habilitation thesis is about a selection of my works concerned with the study of
regularity for Partial Differential Equations, with a focus on equations stemming from fluid …

We derive pointwise best-approximation results for the stationary Stokes problem. For the
instationary problem, we show approximation error estimates pointwise in time and in L2 in …