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 consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain
Ω subject to homogeneous Dirichlet boundary conditions. We prove L p-resolvent estimates …

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 …

This paper develops L pL q decay estimates of the gradient of the Stokes semigroup (T (t))
t≥ 0 generated by the negative of the Stokes operator in exterior Lipschitz domains Ω⊂ R n …

We show that the Stokes operator defined on L σ p (Ω) for an exterior Lipschitz domain Ω⊂
R n (n≥ 3) admits maximal regularity provided that p satisfies| 1/p− 1/2|< 1/(2 n)+ ε for some …

Existence and uniqueness of solutions to the Navier-Stokes equations in dimension two with
forces in the space L q ((0, T); W− 1, p (Ω)) for p and q in appropriate parameter ranges are …

Abstract The Navier–Stokes system ut+(u·∇) u= Δ u+∇ P+ f (x, t),∇· u= 0, is considered
along with homogeneous Dirichlet boundary conditions in a smoothly bounded planar …

We discuss nonlinear nonlocal equations with fractional diffusion describing
electroconvection phenomena in incompressible viscous fluids. We prove the global well …

The Stokes resolvent problem λ u-Δ u+ ∇ ϕ= f λ u-Δ u+∇ ϕ= f with div (u)= 0 div (u)= 0
subject to homogeneous Dirichlet or homogeneous Neumann-type boundary conditions is …

This paper is a development of the results and techniques of the two papers (Carvalho-Neto
and Planas in J Differ Equ 259: 2948–2980, 2015; Oka in J Math Anal Appl 473: 382–407 …