International Cooperation
-
-
Grant: 7AMB16PL060
from 01/01/2017
to 31/12/2018
Grantor: Ministry of Education, Youth and Sports - MŠMT
-
Flow of viscous fluid in time dependent domain
-
-
Objectives:
G1. Global existence of weak solution of full system in time-dependent domain.
Goals: Our goals is the study of the global existence of a weak solution in the case of a bounded or an exterior domains for the Navier or Dirichlet type of boundary conditions. We will use the method introduced in E. Feireisl: Dynamics of viscous compressible fluids, 2004 for fixed domain and we will also apply the penalization method.
G2: Relative entropy inequality.
Goals: We will focus on the derivation of the relative entropy inequality in the case of time-dependent domain. We will use the results from fixed domain introduced in E. Feireisl and A. Novotný: Weak-strong uniqueness for the full Navier-Stokes-Fourier system, 2012.
G3. Singular limits.
Goals We shall study the singular limits in the regime of low Mach number. From this follows that the limit system (target system) is the system of incompressible flow in the time-dependent domain. We will use the results from E. Feireisl, O. Kreml, Š. Nečasová, J. Neustupa, J. Stebel: Incompressible limits of fluids excited by moving boundaries, 2014, where barotropic case was studied, and also the results for fixed domains.
G4: Weak solution of viscous flow around rotating rigid body and his asymptotic behavior.
Goals: We will focus on the problem of existence of weak solution in weighted Lorentz spaces to get the asymptotic behavior of flow around a body. Because of the lack of the regularity in Lp spaces it is necessary to go into more complicated structure of Lorentz spaces, where the integrability of convective term is satisfied. Moreover, we would like to study the relative entropy inequality in the case of compressible flow around rotating body.
-
-
-
Grant: GF17-33849L
from 01/01/2017
to 31/12/2019
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
-
Filters, Ultrafilters and Connections with Forcing
-
-
Objectives:
The project falls within the scope of Set Theory & Foundations of Mathematics, specifically Combinatorial Set Theory and Forcing. We will investigate new combinatorial and forcing methods for constructing ultrafilters with special properties in different models of Set Theory.It will use these methods to answer independence questions about ultrafilters (no P-points with a large continuum or small character filters), structural questions about filters (which ultrafilters/filters contain towers) and questions about the related cardinal invariants (independence number, free sequence number). It is known that current methods cannot answer some of these questions so the project will have to come up with novel ideas. The methods used will include forcing iterations, diamond-like constructions, preservation theorems and methods from descriptive set theory.
-
-
-
Grant: 7AMB17FR053
from 01/01/2017
to 31/12/2018
Grantor: Ministry of Education, Youth and Sports - MŠMT
-
Dynamics of mutli-component fluids
-
-
The goal of the project is studying qualitative properties of a particular class of the so-called energetically weak solutions to complex system of the Navier-Stokes-Fourier type as well as Coupling of these systems with the phase transition equations of the Cahn-Hilliard or Allen-Cahn type. We plan to investigate these problems also in unbounded physical domains in appropriate classes of uniformly bounded functions.
The main goal is obtaining new results in the following directions:
• applications of the relative entropy methods and the consequences concerning stability of the so-called dissipative solutions
• singular limits, in particular the sharp interface limits with rigorous mathematical justification
• long-time dynamics, with a particular emphasis on the existence of bounded absorbing sets, asymptotic compactness of greajectories and the relevant questions concerning the attractors and their structure and complexity
-
-
-
Grant: CNR-16-08
from 05/04/2016
to 31/12/2018
Grantor: Czech Academy of Sciences / CNR Italy
-
Phenomenological modeling of polymeric smart foams with behavior controlled by the magnetic field
-
-
The aim of the collaboration is to develop and test experimentally a reliable mathematical model for magnetic foams taking into account hysteresis effects in the material, with the goal to provide, as output, parameters needed to obtain optimal performance in both "passive" (structural reinforcement and gradient properties) and "active" modes (actuation and control through magnetic field) of lightweight porous polymeric structures reinforced with aligned magnetic particles. The average distribution, size and shape of particles, their magnetic characteristics, and mechanical properties of the foam will be considered as processing parameters. Homogenization techniques will be adopted in order to derive simple constitutive relationships for low computational requirements. The developed constitutive model will be phenomenological, while the governing equations will be based on the magnetic and mechanical balance laws. The development and validation of the model will be performed by comparing predictions with experiments.
-
-
-
Grant: GF16-34860L
from 01/01/2016
to 31/12/2018
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
-
Logic and Topology in Banach spaces
-
-
Objectives:
The project is devoted to the study of topological and geometric properties of Banach spaces and their duals, aiming at a better understanding of their structure. Properties of the weak topology often imply important geometric properties of the Banach space in question. On the other hand, geometric properties of the Banach space often give information about its weak topology. Similar statements are true for duals of Banach spaces with the weak-star topology. We are going to explore this interplay in detail. The main project goals are:
1. Developing new tools for constructing and studying Banach spaces, using techniques from set theory and category theory.
2. Exploring different types of networks and related concepts in weak topologies, determining connections with renorming theory.
Results of Goal 1 will lead to new examples, settling some of the problems concerning interplay between geometric and topological properties of non-separable Banach spaces. Goal 2 will lead to a better understanding of the weak topology and its relations to the geometric structure of a Banach space.
-
-
-
Grant: 7AMB16AT035
from 01/01/2016
to 31/12/2017
Grantor: Ministry of Education, Youth and Sports - MŠMT
-
Performance and thermodynamic aspects of incrementally non-linear constitutive equations of the rate type
-
-
Objectives:
Although first models of hypoplasticity were proposed some decades ago, their properties have not yet been sufficiently understood, neither from the viewpoint of general applicability to large classes of technical problems, nor from the viewpoint of their mathematical well-posedness and numerical complexity. In special cases, however, there is evidence of their strong modeling potential for describing irreversible deformations, in particular in the case of granular or porous solids. The goal of this project is to exploit the complementary knowledge and experience of its participants, and classify the individual models within a larger thermomechanical context. The models will be investigated both analytically and numerically, and the results will be compared with known experimental data published in the literature, which will enable us to decide about their applicability for solving practical problems.
-
