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Basic systems of fluid mechanics. Regularity, stability, structure of solutions.

2014/14/M/ST1/00108

Keywords

Descriptors

  • ST1_11: Równania różniczkowe cząstkowe

Panel

ST1 – Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution

Instytut Matematyczny Polskiej Akademii Nauk

Voivodeship: mazowieckie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Piotr Bogusław Mucha

Number of co-investigators in the project: 7

Call

HARMONIA 6 – announced on 2014-06-16

Amount awarded
468 000 PLN
Project start date
2015-04-14
Project end date
2018-11-13
Project duration
43 months (the same as in the proposal)
Project status
Project settled

Information in the final report

Publication in academic press/journals (20)

  1. Weak and variational entropy solutions to the system describing steady flow of a compressible reactive mixture

    Authors:
    Tomasz Piasecki , Milan Pokorný
    Academic press:
    Nonlinear Analysis (year: 2016, volume: 0, pages: 46050), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.na.2016.12.015 – link to the publication

  2. The Incompressible Navier-Stokes Equations in Vacuum

    Authors:
    RAPHAËL DANCHIN,PIOTR BOGUSŁAW MUCHA
    Academic press:
    Communications on Pure and Applied Mathematics (year: 2019, volume: 7, pages: 1351-1385), Publisher: Wiley
    Status:
    Published

  3. FROM THE HIGHLY COMPRESSIBLE NAVIER-STOKES EQUATIONS TO THE POROUS MEDIUM EQUATION -- RATE OF CONVERGENCE

    Authors:
    B.Haspot, E.Zatorska
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (A) (year: 2016, volume: 36,6, pages: 3107-3123), Publisher: AIMS
    Status:
    Published
    DOI:
    10.3934/dcds.2016.36.3107 – link to the publication

  4. On singular limits arising in the scale analysis of stratified fluid flows

    Authors:
    E.Feireisl, R.Klein, A.Novotny, E.Zatorska
    Academic press:
    Mathematical Models and Methods in Applied Sciences (year: 2016, volume: 26,3, pages: 419-443), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S021820251650007X – link to the publication

  5. On the pressureless damped Euler–Poisson equations with quadratic confinement: Critical thresholds and large-time behavior

    Authors:
    Jose A. Carrillo, Young-Pil Choi, Ewelina Zatorska
    Academic press:
    Mathematical Models and Methods in Applied Sciences (year: 2016, volume: 26, pages: 2311-2340), Publisher: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S0218202516500548 – link to the publication

  6. Existence and Uniqueness of Strong Stationary Solutions

    Authors:
    Ondřej Kreml, Piotr B. Mucha, and Milan Pokorný
    Academic press:
    in : Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (year: 2016, volume: 1, pages: 19725), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/978-3-319-10151-4_65-1 – link to the publication

  7. Finite-Energy Solutions for Compressible Two-Fluid Stokes System

    Authors:
    Didier Bresch , Piotr B. Mucha & Ewelina Zatorska
    Academic press:
    Arch. Rational Mech. Anal. (year: 2018, volume: x, pages: 15707), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00205-018-01337-z – link to the publication

  8. Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Large Mean Flow

    Authors:
    J.Cyranka, P.B.Mucha, E.T.Titi,P.Zgliczynski
    Academic press:
    Physica D. Nonlinear Phenomena (year: 2018, volume: 369, pages: 18-29), Publisher: SciDirect
    Status:
    Published

  9. Local existence of strong solutions and weak-strong uniqueness for the compressible Navier-Stokes system on moving domains

    Authors:
    Ondřej Kreml, Šárka Nečasová,Tomasz Piasecki
    Academic press:
    Proceedings of the Royal Society of Edinburgh, (year: 2019, volume: ., pages: 16803), Publisher: RSE
    Status:
    Published
    DOI:
    10.1017/prm.2018.165 – link to the publication

  10. STEADY SOLUTIONS TO VISCOUS SHALLOW WATER EQUATIONS. THE CASE OF HEAVY WATER

    Authors:
    S AXMANN, PIOTR B MUCHA, M POKORNY
    Academic press:
    COMMUN. MATH. SCI. (year: 2017, volume: 15, pages: 1385--1402), Publisher: International Press
    Status:
    Published

  11. BETWEEN HOMOGENEOUS AND INHOMOGENEOUS NAVIER-STOKES SYSTEMS: THE ISSUE OF STABILITY

    Authors:
    PIOTR B. MUCHA, LIUTANG XUE, AND XIAOXIN ZHENG
    Academic press:
    Journal of Differential Equations (year: 2019, volume: 267, pages: 307-363), Publisher: SciDirect
    Status:
    Published

  12. Regular solutions to the fractional Euler alignment system in the Besov spaces framework

    Authors:
    Raphaël Danchin, Piotr B. Mucha, Jan Peszek, Bartosz Wróblewski
    Academic press:
    Mathematical Models and Methods in Applied Sciences (year: 2019, volume: x, pages: 46053), Publisher: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S0218202519500040 – link to the publication

  13. On strong dynamics of compressible two-component mixture flow

    Authors:
    Tomasz PIASECKI, Yoshihiro SHIBATA and Ewelina ZATORSKA
    Academic press:
    SIAM Journal on Mathematical Analysis (year: 2019, volume: 51, pages: 2793-2849), Publisher: SIAM
    Status:
    Published

  14. Existence of weak solutions for compressible Navier–Stokes equations with entropy transport

    Authors:
    David Maltese, Martin Michálek , Piotr B. Mucha , Antonin Novotný, Milan Pokorný , Ewelina Zatorska
    Academic press:
    J. Differential Equations (year: 2016, volume: 261, pages: 4448-4485), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2016.06.029 – link to the publication

  15. Incompressible limit of the Navier—Stokes model with a growth term

    Authors:
    Nicolas Vauchelet, Ewelina Zatorska
    Academic press:
    Nonlinear Analysis (year: 2017, volume: 163, pages: 34-59), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.na.2017.07.003 – link to the publication

  16. From compressible to incompressible inhomogeneous flows in the case of large data

    Authors:
    Raphaël Danchin and Piotr Bogusław Mucha
    Academic press:
    Tunisian Journal of Mathematics (year: 2019, volume: 1, pages: 127-149), Publisher: MSP
    Status:
    Published
    DOI:
    10.2140/tunis.2019.1.127 – link to the publication

  17. COMPRESSIBLE NAVIER-STOKES SYSTEM : LARGE SOLUTIONS AND INCOMPRESSIBLE LIMIT

    Authors:
    RAPHAËL DANCHIN AND PIOTR BOGUS LAW MUCHA
    Academic press:
    Advances in Mathematics (year: 2017, volume: 320, pages: 904-925), Publisher: Elsevier
    Status:
    Published

  18. On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions

    Authors:
    Tomasz Piasecki and Milan Pokorný
    Academic press:
    Contemporary Mathematics (year: 2018, volume: 710, pages: 223-242), Publisher: AMS
    Status:
    Published

  19. A construction of two different solutions to an elliptic system

    Authors:
    J.Cyranka, P.B.Mucha
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2018, volume: 465, pages: 500-530), Publisher: SciDirect
    Status:
    Published

  20. Steady transport equation in Sobolev-Slobodetskii spaces

    Authors:
    T.Piasecki
    Academic press:
    Colloquium Mathematicum (year: 2018, volume: 154, pages: 65-76), Publisher: IMAPN
    Status:
    Published

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