DCDS-S
On the motion of rigid bodies in an incompressible or compressible viscous fluid under the action of gravitational forces
Bernard Ducomet Šárka Nečasová
The global existence of weak solutions is proved for the problem of the motion of several rigid bodies either in a non-Newtonian fluid of power law type or in a barotropic compressible fluid, under the influence of gravitational forces.
keywords: compressible fluids incompressible fluids Motion of rigid bodies gravitational forces.
DCDS-S
New developments in mathematical theory of fluid mechanics
Eduard Feireisl Šárka Nečasová Reimund Rautmann Werner Varnhorn
Mathematical theory of fluid mechanics is a field with a rich long history and active present. The volume collects selected contributions of distinguished experts in various domains ranging from modeling through mathematical analysis to numerics and practical implementations related to real world problems.

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DCDS
The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body
Reinhard Farwig Ronald B. Guenther Enrique A. Thomann Šárka Nečasová
We derive the fundamental solution of the linearized problem of the motion of a viscous fluid around a rotating body when the axis of rotation of the body is not parallel to the velocity of the fluid at infinity.
keywords: Navier-Stokes problem linearized problem rotating body Fundamental solution wake. translating body
DCDS
On the existence of global strong solutions to the equations modeling a motion of a rigid body around a viscous fluid
Šárka Nečasová Joerg Wolf
The paper deals with the global existence of strong solution to the equations modeling a motion of a rigid body around viscous fluid. Moreover, the estimates of second gradients of velocity and pressure are given.
keywords: estimate of second gradient of the pressure. motion of rigid body estimates of second gradient of velocity field strong solutions Incompressible fluid
DCDS-S
Stokes and Oseen flow with Coriolis force in the exterior domain
Šárka Nečasová
In the paper we will study the problem of steady viscous linear case with Coriolis force in the exterior domain.
keywords: Exterior domain Coriolis. force Stokes problem Oseen Problem
DCDS-B
Thermalization time in a model of neutron star
Bernard Ducomet Šárka Nečasová
We consider an initial boundary value problem for the equation describing heat conduction in a spherical model of neutron star considered by Lattimer et al. We estimate the asymptotic decay of the solution, which provides a plausible estimate for a "thermalization time" for the system.
keywords: one-dimensional symmetry Compressible neutron star. heat conducting fluids
PROC
A linearized system describing stationary incompressible viscous flow around rotating and translating bodies: Improved decay estimates of the velocity and its gradient
Paul Deuring Stanislav Kračmar Šárka Nečasová
We consider a linearization of a model for stationary incompressible viscous ow past a rigid body performing a rotation and a translation. Using a representation formula, we obtain pointwise decay bounds for the velocity and its gradient. This result improves estimates obtained by the authors in a previous article.
keywords: rotating body Navier-Stokes system viscous incompressible ow decay fundamental solution
DCDS
A leading term for the velocity of stationary viscous incompressible flow around a rigid body performing a rotation and a translation
Paul Deuring Stanislav Kračmar Šárka Nečasová

We consider the Navier-Stokes system with Oseen and rotational terms describing the stationary flow of a viscous incompressible fluid around a rigid body moving at a constant velocity and rotating at a constant angular velocity. In a previous paper, we proved a representation formula for Leray solutions of this system. Here the representation formula is used as starting point for splitting the velocity into a leading term and a remainder, and for establishing pointwise decay estimates of the remainder and its gradient.

keywords: Exterior domain viscous incompressible flow rotating body fundamental solution asymptotic expansion Navier-Stokes system
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Preface
Šárka Nečasová Reimund Rautmann Werner Varnhorn
This Volume of Discrete and Continuous Dynamical Systems is dedicated to Professor Vsevolod Aleksevich Solonnikov on the occasion of his 75th birthday.
   He was born on June 8th, 1933 in Leningrad. Working at the Department of the Steklov Mathematical Institute in today St. Petersburg for more than 50 years he has published nearly 250 scientific papers on the theory of partial differential equations and function theory. Moreover, he was teaching for 20 years at the Chair of Mathematical Physics at the Faculty of Mathematics and Mechanics at Leningrad State University. He has many pupils. Under his supervision, two doctoral and eight candidate theses were defended. He regularly participates in international scientific conferences all over the world. He is speaking at least six European languages.

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DCDS-S
A representation formula for linearized stationary incompressible viscous flows around rotating and translating bodies
Paul Deuring Stanislav Kračmar Šárka Nečasová
A Green's formula is proved for solutions of a linearized system describing the stationary flow of a viscous incompressible fluid around a rigid body which is rotating and translating. The formula in question is based on the fundamental solution obtained by integrating the time variable in the fundamental solution of the corresponding evolutionary problem.
keywords: fundamental solution. viscous incompressible flow rotating body

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