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- ItemOn the existence of weak solutions in the context of multidimensional incompressible fluid dynamics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Lasarzik, RobertWe define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. This concept is shown to be equivalent to weak solutions with energy conservation. Via a standard Galerkin discretization, we prove the existence of energy-variational solutions and thus weak solutions in any space dimension for the Navier--Stokes equations. In the limit of vanishing viscosity the same assertions are deduced for the incompressible Euler system. Via the selection criterion of maximal dissipation we deduce well-posedness for these equations.
- ItemMaximal dissipative solutions for incompressible fluid dynamics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Lasarzik, RobertWe introduce the new concept of maximal dissipative solutions for the Navier--Stokes and Euler equations and show that these solutions exist and the solution set is closed and convex. The concept of maximal dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique. A maximal dissipative solution is defined as the minimizer of a convex functional and we argue that this definition bears several advantages.
- ItemSpinodal dewetting of thin films with large interfacial slip : implications from the dispersion relation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Rauscher, Markus; Blossey, Ralf; Münch, Andreas; Wagner, BarbaraWe compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For PS films on OTS covered Si wafers (with slip length $bapprox 1,mu$m) we predict a 20% shift of the position of the maximum of the power spectrum which should be detectable in experiments.