Constructing a culture of solidarity: London and the British coalfields in the long 1970s

This article explores relationships of solidarity constructed between London and the British coalfields from 1968 until the 1984–1985 miners’ strike. Foregrounding the development of a culture of solidarity over this period resituates the support movement during the 1984–1985 strike as embedded in longer-term relationships, which suggests a more equal relationship between coalfield and metropolitan activists than is given by focusing narrowly on the year itself. I argue that a spatially and temporally dynamic sense of the development of these relationships allows us to better grasp the potentially mutual nature of solidarity. Thinking about the construction of this culture of solidarity can contribute significantly to understanding the nature of labour agency. I emphasise the generative nature of solidarity, particularly the ways in which the spatial and social boundaries of the labour movement were challenged through solidarity relationships, allowing in some instances a more diverse conception of working-class politics

Incompressible Euler Equations and the Effect of Changes at a Distance

Because pressure is determined globally for the incompressible Euler equations, a localized change to the initial velocity will have an immediate effect throughout space. For solutions to be physically meaningful, one would expect such effects to decrease with distance from the localized change, giving the solutions a type of stability. Indeed, this is the case for solutions having spatial decay, as can be easily shown. We consider the more difficult case of solutions lacking spatial decay, and show that such stability still holds, albeit in a somewhat weaker form.Comment: Revised statement of Theorem 1 to include a missing definitio

Boundary layer analysis of the Navier-Stokes equations with Generalized Navier boundary conditions

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1, 1) tensor on the boundary. When the tensor is a multiple of the identity we obtain Navier boundary conditions, and when the tensor is the shape operator we obtain conditions in which the vorticity vanishes on the boundary. By constructing an explicit corrector, we prove the convergence of the Navier-Stokes solutions to the Euler solution as the viscosity vanishes. We do this both in the natural energy norm with a rate of order $\epsilon^{3/4}$ as well as uniformly in time and space with a rate of order $\epsilon^{3/8 - \delta}$ near the boundary and $\epsilon^{3/4 - \delta'}$ in the interior, where $\delta, \delta'$ decrease to 0 as the regularity of the initial velocity increases. This work simplifies an earlier work of Iftimie and Sueur, as we use a simple and explicit corrector (which is more easily implemented in numerical applications). It also improves a result of Masmoudi and Rousset, who obtain convergence uniformly in time and space via a method that does not yield a convergence rate.Comment: Additional references and several typos fixe