Abstrakt: We study slow-fast systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. The focus will be on the Navier-Stokes equations, although the t
Abstrakt: We study a finite-element based space-time discretisation for the 2D stochastic Navier--Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal c
Abstrakt: I will discuss certain homogenization and large-scale regularity results in degenerate and/or singular random media. First I describe a quenched invariance principle and local limit theorem
Abstrakt: The intermediate long wave equation (ILW) models water waves of finite depth, connecting the Benjamin-Ono equation (deep-water limit) and the KdV equation (shallow-water limit). Convergence
Abstrakt: We study the 2D Navier-Stokes equation with transport noise subject to periodic boundary conditions. Our main result is an error estimate for the time-discretisation showing a convergence ra
Abstract: Homotopy methods are attractive due to their capability of solving difficult optimization and optimal control problems. The underlying idea is to construct a homotopy, which may be considere
Abstrakt: For a prescribed deterministic kinetic energy we use convex integration to construct analytically weak and probabilistically strong solutions to the 3D in-compressible Navier-Stokes equation
Abstract: We analyse the finitely extensible nonlinear elastic (FENE) dumbbell model of Warner-type for an incompressible polymer fluid (described by the Navier– Stokes–Fokker–Planck equations) intera
Abstrakt: We consider nonlocal equations with irregular coefficients and present pointwise gradient estimates in terms of Riesz potentials as well as estimates in terms of certain fractional maximal f
Abstrakt: Linear Maxwell equations for transverse magnetic (TM) polarized fields support single frequency surface plasmon polaritons (SPPs) localized at the interface of a metal and a dielectric. Meta
