Milan Pokorny - Academia.edu (original) (raw)

Teaching Documents by Milan Pokorny

The list of abstracts and papers presented at the Summer-school and workshop of the ERCOFTAC, Ins... more The list of abstracts and papers presented at the Summer-school and workshop of the ERCOFTAC, Inst. of Mathematics CAS, Pittsburg Univ. USA and Czech Technical Univertity, is presented for future meetings of the Pan European Laboratory on Non Homogeneous Turbulence (ERCOFTAC).
A list of contributions compiled by Tomas Bodnar et al. may be found at: http://www.prague-sum.com/site/page/view/download.

Here only Workshop presentations are resumed;

Dagmar Medková / Robin problem for the Oseen system
Milan Pokorný / A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner–Riesz Multipliers
Philippe Fraunie / Two phase flow modeling
Adélia Sequeira / An Overview of Some Mathematical Models for Blood Coagulation
David Wegmann / An Improved Energy Inequality for Weak Solutions of the Navier-Stokes Equations
Jonas Sauer / Maximal Lp-Regularity of the Spatially Periodic Stokes Operator
Petr Sváček / On the conservation of the energy for incompressible flow interacting with solid bodies/particles
Hana Mizerová / Existence, uniqueness and approximation of the diffusive Peterlin viscoelastic model
Peter Otčenáš / A numerical approximation of an equation of the wall in the fluid-structure interaction problem
Evgeniya Stepanova / Flow Pattern Comparison of Miscible and Solid Markers in Compound Vortex
Vladimír Hric / Numerical Solution of Transonic Wet Steam Flow with Non-equilibrium Condensation
Viktor Šíp / Development of FVM Solver for ABL Flows
Nikolay Shevtsov / Visualization of waves on the free surface of the compound vortex
Tobias Seitz / Flow Reconstruction from MRV Measurements
Xiaoxin Zheng / Time-dependent singularities in the Navier-Stokes system
Benyahia Mohamed / On the weak solutions to the Fluid/Rigid Body interaction problem
Johannes Brand / Fluid Flows & Floating Bodies
Joana Silva / The Impact of the Sea-level Rise in the Hydromorphology of Alluvial Rivers
Giusy Mazzone / On the inertial motions of liquid-filled rigid body with slip boundary conditions
Tomoyuki Nakatsuka / On uniqueness of symmetric Navier-Stokes flows around a body in the plane
Václav Mácha / Self-propelled motion in a viscous compressible fluid
David Wegmann / An Improved Energy Inequality for Weak Solutions of the Navier-Stokes Equations
Irina Denisova / On energy inequality for evolution problem for two fluids of different types without surface tension
Eliška Cézová / Exploratory analysis of meteorological data measured in opencast coal mine
Luboš Matějíček / On the experimental and numerical study of dust dispersion in complex terrain
Jiří Neustupa / On steady solutions of the Bénard problem in a two dimensional quadrangular cavity
Ondřej Kreml / On bounded solutions to the compressible isentropic Euler system
Martin Kalousek / Homogenization of a non-Newtonian flow through a porous medium
Jose Manuel Redondo / Lift off and turbidity currents in the environment
Jose Manuel Redondo / PIV of convective complex flows driven by thermoelectric heat fluxes
David Maltese / Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations

Papers by Milan Pokorny

Applications of Mathematics

Mathematica Bohemica

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 126 (2001) MATHEMATICA BOHEMICA No. 2, 469-481

Applications of Mathematics, 2002

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz 47 (2002)

Journal of Mathematical Physics, Dec 1, 2009

We improve the regularity criterion for the incompressible Navier-Stokes equations in the full th... more We improve the regularity criterion for the incompressible Navier-Stokes equations in the full three-dimensional space involving the gradient of one velocity component. The method is based on recent results of Cao and Titi ͓see "Regularity criteria for the three dimensional Navier-Stokes equations," Indiana Univ. Math. J. 57, 2643 ͑2008͔͒ and Kukavica and Ziane ͓see "Navier-Stokes equations with regularity in one direction," J. Math. Phys. 48, 065203 ͑2007͔͒. In particular, for s ͓2,3͔, we get that the solution is regular if ٌu 3 L t ͑0,T ; L s ͑R 3 ͒͒, 2/ t +3/ s Յ 23 12 .

An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier--Stokes Equations

J Math Fluid Mech, 2000

We show that if v is an axially symmetric suitable weak solution to the Navier{ Stokes equations ... more We show that if v is an axially symmetric suitable weak solution to the Navier{ Stokes equations (in the sense of L. Caarelli, R. Kohn &amp;amp;amp; L. Nirenberg { see (2)) such that either v (the radial component of v )o r v (the tangential component of v) has a higher regularity than is the regularity following from the denition

Steady compressible Navier-Stokes equations in domains with non-compact boundaries

Math Meth Appl Sci, 2005

ABSTRACT We consider the steady compressible Navier–Stokes equations of isentropic flow in three-... more ABSTRACT We consider the steady compressible Navier–Stokes equations of isentropic flow in three-dimensional domains with several exits to infinity with prescribed pressure drops. On the one hand, when each exit is supposed to contain a cone inside, we shall construct bounded energy weak solution for adiabatic constant γ>3. On the other hand, when the exits do not open sufficiently rapidly, we shall prove a non-existence result. Copyright © 2005 John Wiley & Sons, Ltd.

We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a c... more We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the "back to coordinates map" may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for the Navier-Stokes equations. 1 Introduction Recently there has been interest in some new variables describing the solutions to the Navier-Stokes and Euler equations. These variables go under various names, for example, the magnetization variables, impulse variables, velicity or Kuzmin-Oseledets variables. Let us start by considering the incompressible Euler equations in the entire three-dimensional space, that is, ∂u ∂t + u • ∇u + ∇p = f div u = 0

We improve the regularity criterion for the Navier-Stokes equations proved by He [4]. We show tha... more We improve the regularity criterion for the Navier-Stokes equations proved by He [4]. We show that for the Cauchy problem the Leray-Hopf weak solution is smooth provided ∇u3 ∈ L t (0, T ; L s), 2 t + 3 s ≤ 3 2 .

SIAM Journal on Mathematical Analysis, 2015

We investigate a coupling between the compressible Navier-Stokes-Fourier system and the full Maxw... more We investigate a coupling between the compressible Navier-Stokes-Fourier system and the full Maxwell-Stefan equations. This model describes the motion of chemically reacting heat-conducting gaseous mixture. The viscosity coefficients are density-dependent functions vanishing on vacuum and the internal pressure depends on species concentrations. By several levels of approximation we prove the global-in-time existence of weak solutions on the three-dimensional torus.

Analysis, 2015

We present the study of systems of equations governing a steady flow of polyatomic, heat-conducti... more We present the study of systems of equations governing a steady flow of polyatomic, heat-conducting reactive gas mixture. It is shown that the corresponding system of PDEs admits a weak solution and renormalized solution to the continuity equation, provided the adiabatic exponent for the mixture γ is greater than

Selected works of J. Nečas. PDE, continuum mechanics and regularity (to appear)

Steady flow of viscoelastic fluid past an obstacle – Asymptotic behaviour of solutions

We study steady flows of a certain class of viscoelastic fluids past an obstacle in two and three... more We study steady flows of a certain class of viscoelastic fluids past an obstacle in two and three space dimensions with non-zero velocity prescribed at infinity. Decomposing the original problem into the (modified) Oseen problem and transport equations we prove for sufficiently small data the existence of solutions with almost the same asymptotic properties at infinity as the fundamental solution to the Oseen problem.

On axially symmetric flows in ℝ 3

Proceedings of partial differential equations and applications. A conference held in honor of the 70th birthday of Professor Jindřich Nečas in Olomouc, Czech Republic, December 13–17, 1999

Mathematica Bohemica

Some notes to the transport equation and to the Green formula

Rendiconti del Seminario matematico della Università di Padova

Colloquium Mathematicum, 2015

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like... more We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like µ(D) ∼ |D| p−2 (p > 6 5) regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we are able to prove global existence of weak solution to the corresponding system of partial differential equations.

Improvement of some anisotropic regularity criteria for the Navier--Stokes equations

Discrete and Continuous Dynamical Systems - Series S, 2013

ABSTRACT We consider the incompressible Navier-Stokes equations in the entire three-dimensional s... more ABSTRACT We consider the incompressible Navier-Stokes equations in the entire three-dimensional space. Assuming additional regularity on the components of the vector field ∂ 3 u we show intermediate anisotropic regularity results between the results by I. Kukavica and M. Ziane [J. Math. Phys. 48, No. 6, 065203, 10 p. (2007; Zbl 1144.81373)] and by C. Cao and E. S. Titi [Arch. Ration. Mech. Anal. 202, No. 3, 919–932 (2011; Zbl 1256.35051)] and improve the result from the paper by P. Penel and M. Pokorný [“On anisotropic regularity criteria for the solutions to 3D Navier-Stokes equations”, J. Math. Fluid Mech., 13, 341–353 (2011)].

Elliptic and Parabolic Problems - Proceedings of the 4th European Conference, 2002

We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under t... more We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].

Here only Workshop presentations are resumed;

Applications of Mathematics

Mathematica Bohemica

Applications of Mathematics, 2002

Journal of Mathematical Physics, Dec 1, 2009

An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier--Stokes Equations

J Math Fluid Mech, 2000

Steady compressible Navier-Stokes equations in domains with non-compact boundaries

Math Meth Appl Sci, 2005

SIAM Journal on Mathematical Analysis, 2015

Analysis, 2015

Selected works of J. Nečas. PDE, continuum mechanics and regularity (to appear)

Steady flow of viscoelastic fluid past an obstacle – Asymptotic behaviour of solutions

On axially symmetric flows in ℝ 3

Proceedings of partial differential equations and applications. A conference held in honor of the 70th birthday of Professor Jindřich Nečas in Olomouc, Czech Republic, December 13–17, 1999

Mathematica Bohemica

Some notes to the transport equation and to the Green formula

Rendiconti del Seminario matematico della Università di Padova

Colloquium Mathematicum, 2015

Improvement of some anisotropic regularity criteria for the Navier--Stokes equations

Discrete and Continuous Dynamical Systems - Series S, 2013

Elliptic and Parabolic Problems - Proceedings of the 4th European Conference, 2002

Discrete and Continuous Dynamical Systems - Series S, 2007

We study the steady compressible Navier-Stokes equations in a bounded smooth three-dimensional do... more We study the steady compressible Navier-Stokes equations in a bounded smooth three-dimensional domain, together with the slip boundary conditions. We show that for a certain class of the pressure laws, there exists a weak solution with bounded density (in L ∞ up to boundary).