## FG Numerische Analysis partieller Differentialgleichungen

8 Items

**Time-periodic weak solutions to incompressible generalized Newtonian fluids**

*Abbatiello, Anna* (2021-05-20)

In this study we are interested in the Navier–Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of time-periodic three-dimensional flows.

**Vanishing viscosity limit for the compressible Navier–Stokes system via measure-valued solutions**

*Basarić, Danica* (2020-10-21)

We identify a class of measure-valued solutions of the barotropic Euler system on a general (unbounded) spatial domain as a vanishing viscosity limit for the compressible Navier–Stokes system. Then we establish the weak (measure-valued)–strong uniqueness principle, and, as a corollary, we obtain strong convergence to the Euler system on the lifespan of the strong solution.

**On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functions**

*Yserentant, Harry* (2020-07-31)

This paper deals with the equation - Δ u + μ u = f on high-dimensional spaces R^m where μ is a positive constant. If the right-hand side f is a rapidly converging series of separable functions, the solution u can be represented in the same way. These constructions are based on approximations of the function 1/ r by sums of exponential functions. The aim of this paper is to prove results of simi...

**Semiflow selection to models of general compressible viscous fluids**

*Basarić, Danica* (2020-11-23)

We prove the existence of a semiflow selection with range the space of càglàd, i.e. left-continuous and having right-hand limits functions defined on [0,\infty) and taking values in a Hilbert space. Afterwards, we apply this abstract result to the system arising from a compressible viscous fluid with a barotropic pressure of the type aϱ^γ, γ ≥ 1 , with a viscous stress tensor being a nonlinear ...

**Semiflow selection for the compressible Navier–Stokes system**

*Basarić, Danica* (2020-04-30)

Although the existence of dissipative weak solutions for the compressible Navier–Stokes system has already been established for any finite energy initial data, uniqueness is still an open problem. The idea is then to select a solution satisfying the semigroup property , an important feature of systems with uniqueness. More precisely, we are going to prove the existence of a semiflow selection i...

**On a multivalued differential equation with nonlocality in time**

*Eikmeier, André ; Emmrich, Etienne* (2020-05-05)

The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of convolution type with exponential decay. The two operators act on different Banach spaces where one is not embedded in the other. The set-valued right-hand sid...

**On Weak (Measure-Valued)–Strong Uniqueness for Compressible Navier–Stokes System with Non-monotone Pressure Law**

*Chaudhuri, Nilasis* (2020-02-24)

In this paper our goal is to define a renormalized dissipative measure-valued (rDMV) solution of compressible Navier–Stokes system for fluids with non-monotone pressure–density relation. We prove existence of rDMV solutions and establish a suitable relative energy inequality. Moreover we obtain the weak (measure-valued)–strong uniqueness property of this rDMV solution with the help of relative ...

**Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear**

*Päschke, Eileen ; Marschalik, Patrik ; Owinoh, Antony Z. ; Klein, Rupert* (2012)

A strongly tilted, nearly axisymmetric vortex in dry air with asymmetric diabatic heating is analysed here by matched asymptotic expansions. The vortex is in gradient wind balance, with vortex Rossby numbers of order unity, and embedded in a quasigeostrophic (QG) background wind with weak vertical shear. With wind speeds of 60–120 km h-1, such vortices correspond to tropical storms or nascent h...