A necessary condition of potential blowup for the Navier–Stokes system in half-space

Assuming that T is a potential blow up time for the Navier–Stokes system in andreals;3+, we show that the norm of the velocity field in the Lorenz space L3,q with q andlt; andinfin; goes to andinfin; as time t approaches T.</p

The role of diet in the aetiopathogenesis of inflammatory bowel disease

Crohn’s disease and ulcerative colitis, collectively known as IBD, are chronic inflammatory disorders of the gastrointestinal tract. Although the aetiopathogenesis of IBD is largely unknown, it is widely thought that diet has a crucial role in the development and progression of IBD. Indeed, epidemiological and genetic association studies have identified a number of promising dietary and genetic risk factors for IBD. These preliminary studies have led to major interest in investigating the complex interaction between diet, host genetics, the gut microbiota and immune function in the pathogenesis of IBD. In this Review, we discuss the recent epidemiological, gene–environment interaction, microbiome and animal studies that have explored the relationship between diet and the risk of IBD. In addition, we highlight the limitations of these prior studies, in part by explaining their contradictory findings, and review future directions

Local regularity for suitable weak solutions of the Navier-Stokes equations

A class of conditions sufficient for local regularity of suitable weak solutions of the non-stationary three-dimensional Navier-Stokes equations is discussed. The corresponding results are formulated in terms of functionals invariant with respect to the scaling of the Navier-Stokes equations. The well-known Caffarelli-Kohn-Nirenberg condition is contained in the class as a particular case