Weak-strong uniqueness property for the full Navier-Stokes-Fourier system

The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within the class of weak solutions

Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers become small or large enough. We discuss the problem in the framework of global-in-time solutions for both the primitive and the target system. © 2010 Springer Basel AG

Representationalism versus anti-representationalism: a debate for the sake of appearance

Item does not contain fulltextIn recent years the cognitive science community has witnessed the rise of a new, dynamical approach to cognition. This approach entails a framework in which cognition and behavior are taken to result from complex dynamical interactions between brain, body, and environment. The advent of the dynamical approach is grounded in a dissatisfaction with the classical computational view of cognition. A particularly strong claim has been that cognitive systems do not rely on internal representations and computations. Focusing on this claim, we take as a starting point a question recently raised by Cliff and Noble: "... if evolution did produce a design that used internal representations, how would we recognize it?" (Knowledge-based vision and simple visual machines, Philosophical Transactions of the Royal Society: Biological Sciences, 352, 1165-1175, 1997). We will argue that cognitive science lacks a proper operationalization of the notion of representation, and therefore is unable to ftuitfully discuss whether a particular system has representations or not. A basic method to detect representations in a physical system, grounded in isomorphism, turns out to be quite unconstrained. We will look at a practical example of this problem by examining the debate on whether or not van Gelder's (What might cognition be, if not computation? Journal of Philosophy, 92, 345-381, 1995) controversial example of the Watt Governor is representational. We will conclude that cognitive science, as of yet, has no empirically applicable means to answer Cliff and Noble's question unequivocally. This makes the recent representationalism vs. anti-representationalism debate a debate for the sake of appearance

Public health policy, evidence, and causation. Lessons from the studies on obesity

The paper addresses the question of how different types of evidence ought to inform public health policy. By analysing case studies on obesity, the paper draws lessons about the different roles that different types of evidence play in setting up public health policies. More specifically, it is argued that evidence of difference-making supports considerations about ‘what works for whom in what circumstances’, and that evidence of mechanisms provides information about the ‘causal pathways’ to intervene upon