euler equations

Stable and Unstable Singularities in Navier-Stokes ?

Categories Nonlinear Optimization, Robust Optimization Tags , ,

This document provides an extended and rigorous framework dedicated to the geometric analysis of the 3D incompressible Navier-Stokes equations \cite{ESS2003}. We comprehensively develop geometric proofs related to decay estimates, blow-up profiles, and the foundational partial regularity theory of Caffarelli, Kohn, and Nirenberg (CKN). We examine in detail the Hausdorff dimension of potential singular sets, local … Read more

Nonlinear Optimization of District Heating Networks

Categories Applications - Science and Engineering, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing … Read more