8 citations · 13 across the 9 of their papers we have counts for
9 papers
Time-asymptotics of a heated string
Piotr Michał Bies, Tomasz Cieślak
In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a mode…
Linear instability of symmetric logarithmic spiral vortex sheets
Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański
We consider Alexander spirals with branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the (…
Time-zero limits of Kaden's spirals and 2D Euler
Bartosz Bieganowski, Tomasz Cieślak, Jakub Siemianowski
The present note is devoted to the studies of the relation of the time-zero limits of Kaden's spirals and the 2D Euler equation. It is shown that the time-zero limits of Kaden's sp…
Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity
Piotr Michał Bies, Tomasz Cieślak
We construct unique regular solutions to the minimal nonlinear system of the 1d thermoelasticity. The obtained solution has a positive temperature. Our approach is based on an esti…
On the existence of global solutions for the 3D chemorepulsion system
Tomasz Cieślak, Mario Fuest, Karol Hajduk +1
In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dime…
Global weak solutions in nonlinear 3D thermoelasticity
Tomasz Cieślak, Boris Muha, Srđan Trifunović
Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the posi…
Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations
T. Cieślak, P. Kokocki, W. S. Ożański
We consider solutions of the 2D incompressible Euler equation in the form of cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are…
Magnetostatic levitation and two related linear PDEs in unbounded domains
Bartosz Bieganowski, Tomasz Cieślak, Jakub Siemianowski
We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a sol…
Well-posedness of logarithmic spiral vortex sheets
T. Cieślak, P. Kokocki, W. S. Ożański
We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aero-dynamik, 1922)…