We consider the Cauchy problem for incompressible Navier-Stokes equations ut + u∇xu − ∆xu + ∇xp = 0, divu = 0 in Rd×R+ with initial data a ∈ L(R), and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have tD t D n xu ∈ L(R × (0, T )), as long as the ‖u‖Ld+2 x,t (Rd×(0,T )) stays finite.

The endosomal sorting complex required for transport (ESCRT) complexes sort ubiquitinated membrane proteins into multivesicular bodies, which is a key step in the lysosomal degradation pathway. Shields et al. (Shields, S.B., A.J. Oestreich, S. Winistorfer, D. Nguyen, J.A. Payne, D.J. Katzmann, and R. Piper. 2009. J. Cell Biol. 185:213-224) identify a new ubiquitin-binding site in ESCRT-I and pr...

STOCK DEFINITION AND GEOGRAPHIC RANGE The common dolphin may be one of the most widely distributed species of cetaceans, as it is found world-wide in temperate, tropical, and subtropical seas. In the North Atlantic, common dolphins appears to be present along the coast over the continental shelf along the 200-300 m isobaths or over prominent underwater topography from 50E N to 40ES latitude (Ev...