This course is a short introduction to the mathematical theory of the motion of viscous fluids. We introduce the concept of weak solution to the Navier-Stokes-Fourier system and discuss its basic properties. In particular, we construct the weak solutions as a suitable limit of a mixed numerical scheme based on a combination of the finite volume and finite elements method. The question of stability and robustness of various classes of solutions is addressed with the help of the relative (modulated) energy functional. Related results concerning weak-strong uniqueness and conditional regularity of weak solutions are presented. Finally, we discuss the asymptotic limit when viscosity of the fluid tends to zero. Several examples of ill- posedness...
summary:The paper contains the proof of global existence of weak solutions to the mixed initial-boun...
Abstract: We study a Navier-Stokes system which is motivated by models for electrorheological fluids...
AbstractWe study problems of vanishing viscosity limit of statistical solutions of the Navier-Stokes...
AbstractWe develop a mathematical theory of compressible, viscous, and heat conducting fluids based ...
In this work, we introduce a notion of dissipative weak solution for a system describing the evoluti...
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. Th...
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. Th...
This work is devoted to the study of the main models which describe the motion of incompressible flu...
This thesis contains a set of articles concerned with flow of a viscous, compressible and heat condu...
This thesis contains a set of articles concerned with flow of a viscous, compressible and heat condu...
We consider the Cauchy problem for a system of partial differential equations that describes the dyn...
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible ...
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible ...
We consider the Cauchy problem for a system of partial differential equations that describes the dyn...
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible ...
summary:The paper contains the proof of global existence of weak solutions to the mixed initial-boun...
Abstract: We study a Navier-Stokes system which is motivated by models for electrorheological fluids...
AbstractWe study problems of vanishing viscosity limit of statistical solutions of the Navier-Stokes...
AbstractWe develop a mathematical theory of compressible, viscous, and heat conducting fluids based ...
In this work, we introduce a notion of dissipative weak solution for a system describing the evoluti...
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. Th...
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. Th...
This work is devoted to the study of the main models which describe the motion of incompressible flu...
This thesis contains a set of articles concerned with flow of a viscous, compressible and heat condu...
This thesis contains a set of articles concerned with flow of a viscous, compressible and heat condu...
We consider the Cauchy problem for a system of partial differential equations that describes the dyn...
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible ...
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible ...
We consider the Cauchy problem for a system of partial differential equations that describes the dyn...
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible ...
summary:The paper contains the proof of global existence of weak solutions to the mixed initial-boun...
Abstract: We study a Navier-Stokes system which is motivated by models for electrorheological fluids...
AbstractWe study problems of vanishing viscosity limit of statistical solutions of the Navier-Stokes...