We consider the mixing behaviour of the solutions of the continuity equation associated with a divergence-free velocity field. In this announcement we sketch two explicit examples of exponential… (More)

We establish a decomposition of Besov-Morrey spaces in terms of smooth “wavelets” obtained from a Littlewood-Paley partition of unity, or more generally molecules concentrated on dyadic cubes. We… (More)

In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a 4 prescribed time-dependent rotation of the boundary about… (More)

We study a special class of solutions to the 3D Navier-Stokes equations ∂tu +∇uνu +∇p = ν∆u , with no-slip boundary condition, on a domain of the form Ω = {(x, y, z) : 0 ≤ z ≤ 1}, dealing with… (More)

We consider 3D Navier-Stokes flows with no-slip boundary condition in an infinitely long pipe with circular cross section. The velocity fields we consider are independent of the variable… (More)

Let μ ∈ Z+ be arbitrary. We prove a well-posedness result for mixed boundary value/interface problems of second-order, positive, strongly elliptic operators in weighted Sobolev spaces K a (Ω) on a… (More)

We prove a regularity result for the anisotropic elasticity equation Pu := div ` C · ∇u) = f , with mixed (displacement and traction) boundary conditions Lk on a curved polyhedral domain Ω ⊂ R 3 in… (More)

palenstrophy flows Evelyn Lunasin, Zhi Lin, a) Alexei Novikov, Anna Mazzucato, and Charles R. Doering Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 Department of Mathematics,… (More)

We establish the mathematical validity of the Prandtl boundary layer theory for a family of (nonlinear) parallel pipe flow. The convergence is verified under various Sobolev norms, including the… (More)

We construct closed-form asymptotic formulas for the Green’s function of parabolic equations (e.g. Fokker-Planck equations) with variable coefficients in one space dimension. More precisely, let u(t,… (More)