Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension

In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in water. Our main result is a weak-strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier-Stokes equation: As long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities the concept of varifold solutions - whose global in time existence has been shown by Abels [2] for general initial data - does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy.Comment: 104 page

Profit Limitation Controls Prior to the Present War

In March 2014, four organisations, the Global School (Den Globala Skolan), the Swedish International Centre of Education for Sustainable Development (SWEDESD) at Uppsala University, the Swedish National Commission for UNESCO (Svenska Unescorådet) and WWF-Sweden commissioned Anders Jidesjö, senior lecturer and researcher at Linköping University, to undertake a study of the Swedish experience in the domain of Education for Sustainable Development (ESD) over the last 10 years by analysing relevant background documentation and reports as well as information gathered through interviews with key informants. This report presents the result of this study. An earlier version served as background document for the "ESD – Call for Action" event on 3 June 2014 (see also below). The current version has benefited from incorporating factual information and insights presented during that event. The report was commissioned in view of the UNESCO World Conference on Education for Sustainable Development, scheduled for 11-12 November in Aichi-Nagoya, Japan. This conference will mark the end of the UN Decade on Education for Sustainable Development, 2005-2014. The four organisations considered that the official Swedish position at the Nagoya Conference would be strengthened if informed by the experiences and insights of Swedish pre-schools, schools, universities, municipalities and public, private and non-governmental organizations that over the last ten years and longer have engaged in education and learning for sustainable development. The official Swedish position would also be bolstered by having politicians, policy makers and experts reflect on these experiences and formulate recommendations for reinforced policy and accelerated and effective practice and research in the ESD domain. To this effect, the four organizations organized the event "ESD – Call for Action", on 3 June at Blåsenhus, Uppsala University. It brought together 120 representatives of Swedish ESD-related practitioners, researchers and policy makers who together formulated an extensive set of recommendations that are meant to support the Swedish delegation attending the Nagoya Conference. The report and the 3 June recommendations will be made available to the participants of a second event "Making ESD Action Possible", scheduled for 27 August, 2014 at Rosenbad Conference Centre, Stockholm. This event is expected to assemble 140 Swedish ESD-related politicians, policy makers, researchers and practitioners. The combined recommendations formulated by the participants during the two events will be submitted to the official Swedish delegation to the Nagoya Conference. August 2014 Den Globala Skolan (the Global School), Svenska Unescorådet (Swedish National Commission for UNESCO), Swedish International Centre of Education for Sustainable Development (SWEDESD) at Uppsala University, WWF-Swede

Stability Conditions and Lagrangian Cobordisms

In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,\omega)$ induces a stability condition on the derived Fukaya category of Lagrangian cobordisms $D\mathcal{F}uk(\mathbb{C} \times M)$. In addition, using stability conditions, we provide general conditions under which the homomorphism $\Theta: \Omega_{Lag}(M)\to K_0(D\mathcal{F}uk(M))$, introduced by Biran and Cornea, is an isomorphism. This yields a better understanding of how stability conditions affect $\Theta$ and it allows us to elucidate Haug's result, that the Lagrangian cobordism group of $T^2$ is isomorphic to $K_0(D\mathcal{F}uk(T^2))$.Comment: 53 pages, 3 figures, expansions and revisions, improvement of expositio