61 citations · 341 across the 41 of their papers we have counts for
50 papers
Range Failure, Resolvent Growth, and Resonance in Partially Dissipative Systems
Boris Muha, Sebastian Schwarzacher, Justin T. Webster
We introduce several notions of resonance for systems exhibiting weak or partial dissipation: , with the generator of a strongly stable semigroup on a Hi…
Well-posedness theorems in fluid-structure interaction: perfectly elastic shells
Dominic Breit, Prince Romeo Mensah, Sebastian Schwarzacher +1
In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell…
The Stokes problem with Navier boundary conditions in irregular domains
Dominic Breit, Sebastian Schwarzacher
We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including…
Time-Periodic Solutions for Hyperbolic-Parabolic Systems
Stanislav Mosny, Boris Muha, Sebastian Schwarzacher +1
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective -dimensional spatial domain…
Existence of strong solutions for a perfect elastic beam interacting with Navier-Stokes equations
Sebastian Schwarzacher, Pei Su
A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperboli…
Ladyzhenskaya-Prodi-Serrin condition for fluid-structure interaction systems
Dominic Breit, Prince Romeo Mensah, Sebastian Schwarzacher +1
We consider the interaction of a viscous incompressible fluid with a flexible shell in three space dimensions. The fluid is described by the three-dimensional incompressible Navier…
Stability and convergence of in time approximations of hyperbolic elastodynamics via stepwise minimization
Antonín Češík, Sebastian Schwarzacher
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two ti…
Time-periodic weak solutions for the interaction of an incompressible fluid with a linear Koiter type shell under dynamic pressure boundary conditions
Claudiu Mîndrilă, Sebastian Schwarzacher
In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equ…
Stability and error estimates of a linear numerical scheme approximating nonlinear fluid-structure interactions
Sebastian Schwarzacher, Bangwei She, Karel Tuma
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We…
Unrestricted deformations of thin elastic structures interacting with fluids
Malte Kampschulte, Sebastian Schwarzacher, Gianmarco Sperone
In this paper we discuss the motion of a beam in interaction with fluids. We allow the beam to move freely in all coordinate directions. We consider the case of a beam situated in…
Injectivity in second-gradient Nonlinear Elasticity
D. Campbell, S. Hencl, A. Menovschikov +1
We study injectivity for models of Nonlinear Elasticity that involve the second gradient. We assume that is a domain, satisfie…
Time-periodic weak solutions for an incompressible Newtonian fluid interacting with an elastic plate
Claudiu Mîndrilă, Sebastian Schwarzacher
Under the action of a time-periodic external forces we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressibl…
Compressible fluids interacting with 3D visco-elastic bulk solids
Dominic Breit, Malte Kampschulte, Sebastian Schwarzacher
We consider the physical setup of a three-dimensional fluid-structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dim…
Construction of a right inverse for the divergence in non-cylindrical time dependent domains
Olli Saari, Sebastian Schwarzacher
We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be Hölder regular in space and evolve continuou…
Variational methods for fluid-structure interaction and porous media
B. Benesova, M. Kampschulte, S. Schwarzacher
In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three…
Navier-Stokes-Fourier fluids interacting with elastic shells
Dominic Breit, Sebastian Schwarzacher
We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a non-linear flexible shell. The fluid is described by the full Navier--Stokes--Fou…
Contactless rebound of elastic bodies in a viscous incompressible fluid
Giovanni Gravina, Sebastian Schwarzacher, Ondřej Souček +1
In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, for w…
A variational approach to hyperbolic evolutions and fluid-structure interactions
Barbora Benešová, Malte Kampschulte, Sebastian Schwarzacher
We introduce a two time-scale scheme which allows to extend the method of minimizing movements to hyperbolic problems. This method is used to show the existence of weak solutions t…
Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
Richard M. Höfer, Karina Kowalczyk, Sebastian Schwarzacher
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles…
On numerical approximations to fluid-structure interactions involving compressible fluids
Sebastian Schwarzacher, Bangwei She
In this paper we introduce a numerical scheme for fluid-structure interaction problems in two or three space dimensions: A flexible elastic plate is interacting with a viscous, com…
Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation
Sebastian Schwarzacher, Matthias Sroczinski
We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic…
Existence of steady very weak solutions to Navier-Stokes equations with non-Newtonian stress tensors
Claudiu Mîndrilă, Sebastian Schwarzacher
We provide existence of very weak solutions and new a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. To…
A reverse Hölder inequality for the gradient of solutions to Trudinger's equation
Olli Saari, Sebastian Schwarzacher
We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly non-linear equation) for the range $p\in [2,\infty…
Two-speed solutions to non-convex rate-independent systems
Filip Rindler, Sebastian Schwarzacher, Juan J. L. Velazquez
We consider evolutionary PDE inclusions of the form \[ -λ\dot{u}_λ+ Δu - \mathrm{D} W_0(u) + f \ni \partial \mathcal{R}_1(\dot{u}) \qquad\text{in ,} \] where $\math…