List of Publications

    Monographs

  1. Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces (with I. Chlebicka, P. Gwiazda, A. Wróblewska-Kamińska), Springer Monographs in Mathematics, 2021 Link
  2. Measure-Valued Solutions for Time-Dependent Partial Differential Equations (with T. Dębiec, P. Gwiazda, E. Wiedemann), in preparation, accepted for Oxford University Press

    3. Peer reviewed journals

  3. From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit (with Charles Elbar, Piotr Gwiazda, Jakub Skrzeczkowski), J. Differential Equations 422, 264–305, 2025 , arXiv:2305.01348
  4. Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations (with Dennis Gallenmüller, Piotr Gwiazda, Jakub Woźnicki), Calc. Var. Partial Differential Equations, 63, no. 2, 47, 2024, arXiv:2304.04050
  5. Dissipative measure-valued solutions to the Euler-Poisson equation (with J.A. Carrillo, T. Dębiec and P. Gwiazda), SIAM J. Math. Anal., 56, no. 1, 304–335, 2024, arXiv:2109.07536
  6. On the high friction limit for the complete Euler system (with Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon) J. Evol. Equ. 24, no. 2, Paper No. 25, 15 pp., 2024
  7. Time periodic motion of temperature driven compressible fluids (with Eduard Feireisl and Piotr Gwiazda), Math. Annalen, 387, no. 3-4, 1603–1627, 2023, Open Access
  8. The Rayleigh-Bénard problem for compressible fluid flows (with Eduard Feireisl), Arch. Ration. Mech. Anal. 247 no. 1, Paper No. 9, 31 pp., 2023, Open Access
  9. Mathematical theory of compressible magnetohydrodynamics driven by non-conservative boundary conditions (with Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon), J. Math. Fluid Mech. 25, no. 4, 84, 2023, Open Access
  10. Dissipative measure-valued solutions for general conservation laws (with Piotr Gwiazda and Ondrej Kreml), Ann. Inst. H. Poincaré Anal. Non Linéaire, no. 3, 683–707, 2020, arXiv:1801.01030
  11. Existence and homogenization of nonlinear elliptic systems in nonreflexive spaces (with Miroslav Bulicek, Piotr Gwiazda and Martin Kalousek), Nonlinear Anal., 194, 111487, 34 pp, 2020, arXiv:1801.07590
  12. Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws (with Claude Bardos, Piotr Gwiazda, Edriss S. Titi and Emil Wiedemann), Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. Volume 475, Issue 2230, 2019 arXiv:1902.07120
  13. A two species hyperbolic-parabolic model of tissue growth (with Piotr Gwiazda and Benoît Perthame), Comm. Partial Differential Equations, 44(12): 1604-1618, 2019, arXiv:1809.01867
  14. Differentiability in perturbation parameter of measure solutions to perturbed transport equation, (with Piotr Gwiazda, Sander C. Hille and Kamila Łyczek), Kinet. Rel. Models, 2019, 12(5): 1093-1108, arXiv:1806.00357
  15. On the Extension of Onsager's Conjecture for General Conservation Laws (with Claude Bardos, Piotr Gwiazda, Edriss S. Titi and Emil Wiedemann), J Nonlinear Sci 29 (2) 2019, s. 501–510, arXiv:1806.02483
  16. Homogenization of nonlinear elliptic systems in nonreflexive Musielak-Orlicz spaces, (with Miroslav Bulicek, Piotr Gwiazda and Martin Kalousek), Nonlinearity 32 (2019), 1073-1110, arxiv.1703.08355
  17. Conservation of energy for the Euler-Korteweg equations (with Tomasz Dębiec, Piotr Gwiazda and Anthanasios Tzavaras), Calc. Var. Partial Differential Equations 57: 160, (2018), Open Access
  18. A note on weak solutions of conservation laws and energy/entropy conservation, (with Piotr Gwiazda and Martin Michálek), Arch. Ration. Mech. Anal., 229 (2018) 1223–1238, arxiv.1706.10154
  19. Existence of global weak solutions to the kinetic Peterlin model (with Piotr Gwiazda, Mária Lukáčová-Medviďová, Hana Mizerová), Nonlinear Anal. Real World Appl. 44 (2018) 465–478, arXiv:1707.02783
  20. Weak solutions for Euler systems with non-local interactions, (with J.A. Carrillo, E. Feireisl and P. Gwiazda), J. Lond. Math. Soc., (2) 95 (2017) 705–724 arXiv:1512.03116
  21. Regularity and Energy Conservation for the Compressible Euler Equations (with E. Feireisl, P. Gwiazda and E. Wiedemann), Arch. Ration. Mech. Anal., 223 (2017), no. 3, 1375–1395 arXiv:1603.05051
  22. High-temperature viscous flows. A case of pudding model (with P.B. Mucha), Nonlinear Anal. 151, 109–125, 2017, arXiv:1601.08047
  23. On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown (with Miroslav Bulicek and Piotr Gwiazda), J. Differ. Equations , 262, no. 1, 313–364, 2017, arXiv:1606.06500
  24. Dissipative measure-valued solutions to the compressible Navier-Stokes system (with E. Feireisl, P. Gwiazda and E. Wiedemann), Calc. Var. Partial Differential Equations , 55, no. 6, 55:141, 2016, arXiv:1512.04852
  25. Transport equation with integral terms (with C. De Lellis and P. Gwiazda), Calc. Var. Partial Differential Equations 55: 128, 2016, arXiv:1602.03193
  26. Analysis of a viscosity model for concentrated polymers, (with Miroslav Bulicek, Piotr Gwiazda and Endre Süli), Math. Models Methods Appl. Sci, Vol. 26, No. 8, 1599–1648, 2016, arXiv:1501.05766
  27. On weak solutions to the 2D Savage-Hutter model of the motion of a gravity driven avalanche flow, (with Eduard Feireisl and Piotr Gwiazda), Comm. Partial Differential Equations, , Volume 41, Issue 5, 759-773, 2016, arXiv:1502.06223
  28. Weak-Strong Uniqueness for Measure-Valued Solutions of Some Compressible Fluid Models, (with Piotr Gwiazda and Emil Wiedemann), Nonlinearity 28 (2015) 3873–3890, arXiv:1503.05246
  29. Thermo-visco-elasticity for Norton-Hoff-type models, (with Filip Klawe and Piotr Gwiazda), Nonlinear Anal. Real World Appl. , Vol. 26, 199-228, 2015, arXiv:1404.1671
  30. Multi-dimensional scalar balance laws with discontinuous flux, (with Piotr Gwiazda, Petra Wittbold and Aleksandra Zimmermann), J. Funct. Anal. 267, no. 8, 2846–2883, 2014, arXiv:1404.2036
  31. Nonlinear parabolic problems in Musielak-Orlicz spaces, Nonlinear Anal. 98, 48-65, 2014 arXiv:1306.2186
  32. Anisotropic parabolic problems with slowly or rapidly growing terms, Colloq. Math, Vol. 134, No 1, 113-130, 2014 arXiv:1307.2337
  33. Multi-dimensional scalar conservation laws with fluxes discontinuous in the unknown and the spatial variable (with Miroslav Bulicek and Piotr Gwiazda), Math. Models Methods Appl. Sci. Vol. 23 (3), 407–439, 2013 Electronic version of an article published as [Math. Models Methods Appl. Sci., Volume 23, No 3, 2013, 407-439] [Article DOI:10.1142/S0218202512500510 ] © [copyright World Scientific Publishing Company] [http://www.worldscientific.com/worldscinet/m3as]
  34. Generalized Stokes system in Orlicz spaces (with Piotr Gwiazda and Aneta Wróblewska), Discrete Contin. Dyn. Syst. Ser. A Vol. 32 (6), 2125–2146, 2012
  35. On unsteady flows of implicitly constituted incompressible fluids (with Miroslav Bulicek, Piotr Gwiazda and Josef Malek), SIAM J. Math. Anal. Vol. 44 (4), 2756 - 2801, 2012 PDF
  36. On scalar hyperbolic laws with discontinuous flux (with Miroslav Bulicek, Piotr Gwiazda and Josef Malek), Math. Models Methods Appl. Sci. Vol. 21 , No. 1, 2011
  37. Monotonicity methods in generalized Orlicz spaces for a class of non-Newtonian fluids (with Piotr Gwiazda and Aneta Wróblewska), Math. Methods Appl. Sci. Vol. 33 No. 2, 125 - 248, 2010,
  38. On steady flows of an incompressible fluids with implicit power-law-like rheology (with Miroslav Bulicek, Piotr Gwiazda and Josef Málek), Adv. Calc. Var. 2, No. 2, 109-136, 2009
  39. On steady non-Newtonian flows with growth conditions in generalized Orlicz spaces (with Piotr Gwiazda), Topol. Methods Nonlinear Anal. 32, No. 1, 103–-114, 2008 PDF
  40. On non-Newtonian fluids with the property of rapid thickening, (with Piotr Gwiazda), Math. Models Methods Appl. Sci. 18, No. 7, 1073--1092, 2008 Electronic version of an article published as [Math. Models Methods Appl. Sci., Volume 18, No 7, 2008, 1073-1092] [Article DOI:10.1142/S021820251100499X] © [copyright World Scientific Publishing Company] [http://www.worldscientific.com/worldscinet/m3as]
  41. On flows of an incompressible fluid with discontinuous power-law-like rheology Comput. Math. Appl. 53, 531--546, 2007 (with Piotr Gwiazda and Josef Málek)
  42. Regularity and uniqueness for the stationary Large Eddy Simulation model. Appl. Math, 51, No. 6, 629--641, 2006
  43. A dynamical approach to Large Eddy Simulation of turbulent flows: existence of weak solutions. Math. Methods Appl. Sci. 28, No. 18 , 2005
  44. Multivalued equations for granular avalanches, Nonlinear Anal., Theory Methods Appl. 62, No.5 (A), 895-912, 2005 (with Piotr Gwiazda).
  45. Large Eddy Simulation turbulence model with Young measures, Appl. Math. Lett. 18 923-929, 2005 (with Piotr Gwiazda).
  46. Large Eddy Simulation. Existence of stationary solutions to a dynamical model, ZAMM Z. Angew. Math. Mech., 85, No.8, 593-604, 2005.
  47. An L^1-stability and uniqueness result for balance laws with multifunctions: a model from the theory of granular media Colloq. Math., 100 (2), 149-162, 2004 (with Piotr Gwiazda).

    48. Proceedings

  48. Relative entropy method for measure-valued solutions in natural sciences (with Tomasz Dębiec, Piotr Gwiazda and Kamila Łyczek), Topol. Methods Nonlinear Anal. 52(1), 311-335, 2018 arXiv:1709.01410
  49. Thermoplasticity for the Mróz's model in the framework of thermodynamically complete systems, Discrete Contin. Dyn. Syst. Ser. S Vol. 7(5), 981-991, 2014 (with Filip Klawe and Piotr Gwiazda).
  50. On the anisotropic Orlicz spaces applied in the problems of continuum mechanics (with Piotr Gwiazda and Piotr Minakowski), Discrete Contin. Dyn. Syst. Ser. S Vol. 6(5), 1291-1306, 2013.
  51. On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph (with Miroslav Bulicek, Piotr Gwiazda, Josef Malek and K.R. Rajagopal), Mathematical Aspects of Fluid Mechanics, London Math. Soc. Lecture Note Ser. 402, 23-51, Cambridge Univ. Press, 2012.
  52. Parabolic equations in anisotropic Orlicz spaces with general N-functions (with Piotr Gwiazda), special Birkhaeuser volume ”Parabolic Problems. The Herbert Amann Festschrift”, Progress in Nonlinear Differential Equations and Their Applications, Vol. 60, 301–311, 2010
  53. Turbulent flows of rapidly thickening fluids (with Piotr Gwiazda and Aneta Wróblewska), Proceedings of Polish-Japanese Days. GAKUTO Vol. 32, 2010
  54. Well-posedness for a class of non-Newtonian fluids with general growth conditions (with Piotr Gwiazda, Andrzej Warzyński and Aneta Wróblewska), Banach Center Publ. 86, 115-128, 2009

    55. Others

  55. Mathematical analysis of Large Eddy Simulation of turbulent flows, Diss. TU Darmstadt, 88 pp., Shaker Verlag Aachen 2004, ISBN 3-8322-3583-3

    56. Preprints

  56. Unconditional stability of radially symmetric steady sates of compressible viscous fluids with inflow/outflow boundary conditions (with Eduard Feireisl and Piotr Gwiazda) arXiv:2412.14577
  57. A tribute to conservation of energy for weak solutions (with Tomasz Dębiec, Piotr Gwiazda), arXiv:1707.09794
If you are interested in any of the papers which are not available for downloading on my webpage, you can e-mail me: aswiercz (at) mimuw.edu.pl

My citation list at Google Scholar and Publons