Dr Wojciech Ożański

Teaching responsibility Fall 2025:

• (MAT320) Introduction to Real Analysis.

Publications:

• (with I.-J. Jeong and L. Martínez-Zoroa) Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation, 2025 (PDF),

• (with I. Kukavica) Exact boundary controllability of the 3D incompressible ideal MHD system, 2024 (PDF),

• (with D. Córdoba and L. Martínez-Zoroa) Instantaneous continuous loss of Sobolev regularity for the SQG equation, 2024, to appear in Adv. Math. (PDF), 

• (with W. Zajączkowski) On the regularity of axially-symmetric solutions to the incompressible Navier-Stokes equations in a cylinder, J. Differ. Equ. 438, 2025 (DOI,PDF),

• (with A. Kumar) A simple proof of linear instability of shear flows with application to vortex sheets, J. Math. Fluid Mech. 27, art. no. 34, 2025 (DOI,PDF),

• An improvement to Prandtl's 1933 model for minimizing induced drag, Appl. Math. Optim. 89, art. no. 39, 2024 (DOI,PDF), 

• (with D. Albritton) Linear and nonlinear instability of vortex columns, 2023 (PDF), 

• (with I. Kukavica and M. Sammartino) The inviscid inflow-outflow problem via analyticity, Arch. Ration. Mech. Anal. 249, art. no. 27, 2025 (DOI,PDF), 

• (with M. Aydin, I. Kukavica and A. Tuffaha) Construction of the free-boundary 3D incompressible Euler flow under limited regularity, J. Differ. Equ. 394, pp. 209-236, 2024 (DOI,PDF),

• (with T. Cieślak and P. Kokocki) Linear instability of symmetric logarithmic spiral vortex sheets, J. Math. Fluid Mech. 26, art. no. 21, 2024 (DOI,PDF),

• (with D. Córdoba and L. Martínez-Zoroa) Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations, Duke Math. J. 173, no. 10, pp. 1931-1971, 2024 (DOI,PDF,VIDEO), 

• (with S. Palasek) Quantitative control of solutions to axisymmetric Navier-Stokes equations in terms of the weak L^3 norm, Ann. PDE 9, art. no. 15, 2023 (DOI,PDF),

• (with I. Kukavica) On a model of an elastic body fully immersed in a viscous incompressible fluid with small data, SIAM J. Math. Anal. 56(1), pp. 746-761, 2024 (DOI,PDF),

• (with T. Cieślak and P. Kokocki) Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XXVI (2025), pp. 301-340 (DOI,PDF),

• (with P. B. Mucha) Global-in-time stability of ground states of a pressureless hydrodynamic model of collective behaviour, Commun. Math. Sci. 21, no. 7, pp. 1937-1959, 2023 (DOI,PDF), 

• (with I. Kukavica) On the global existence for a fluid-structure model with small data, Indiana Univ. Math. J. 72, no. 7, pp. 2701-2731, 2023 (DOI,PDF),

• (with T. Cieślak and P. Kokocki) Well-posedness of logarithmic spiral vortex sheets, J. Differ. Equ. 389, pp. 508-539, 2024 (DOI,PDF),

• Quantitative transfer of regularity of the incompressible Navier-Stokes equations from R^3 to the case of a bounded domain, J. Math. Fluid Mech. 23, art. no. 98, 2021 (DOI,PDF),

• (with I. Kukavica) Local-in-time existence of free-surface 3D Euler flow with H^{2+δ} initial vorticity in a neighborhood of the free boundary, Nonlinearity 36, 636, 2023 (DOI,PDF),

• (with T. Cieślak) A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus, Calc. Var. Partial Differ. Equ. 61, 97, 2022 (DOI,PDF),

• (with I. Kukavica) An anisotropic regularity condition for the 3D incompressible Navier-Stokes equations for the entire exponent range, Appl. Math. Lett. 122, 107298, 2021 (DOI,PDF),

• (with Z. Bradshaw and I. Kukavica) Global weak solutions of the Navier-Stokes equations for intermittent initial data in half-space, Arch. Ration. Mech. Anal. 245, pp. 321-371, 2022 (DOI,PDF),

• (with H. Kwon) Local regularity of weak solutions of the hypodissipative Navier-Stokes equations, J. Funct. Anal. 282(7), 109370, 2022 (DOI,PDF),

• (with J. Burczak and G. Seregin) On regularity properties of a surface growth model, Proc. Roy. Soc. Edinburgh Sect. A 151(6), pp. 1869-1892, 2021 (DOI,PDF),

• Partial regularity of Leray-Hopf weak solutions to the incompressible Navier-Stokes equations with hyperdissipation, Anal. PDE 16, no. 3, pp. 747-783, 2023 (DOI,PDF),

• Weak solutions to the Navier-Stokes inequality with arbitrary energy profiles, Comm. Math. Phys. 374(1), pp. 33-62, 2020 (DOI,PDF),

• A sufficient integral condition for local regularity of solutions to the surface growth model, J. Funct. Anal. 276(10), pp. 2990-3013, 2019 (DOI,PDF),

• (with J. Robinson) Partial regularity for a surface growth model, SIAM J. Math. Anal. 51(1), pp. 228-255, 2019 (DOI,PDF),

• The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness, Lect. Notes Math. Fluid Mech., Birkhäuser/Springer, ISBN  978-3-030-26660-8, 2019, Link; a preprint of the “sharpness part” is available at arXiv:1709.00602 (DOI,PDF),

• (with B. Pooley) Leray's fundamental work on the Navier-Stokes equations: a modern review of “Sur le mouvement d’un liquide visqueux emplissant l’espace”, pp. 113-203, Partial Differential Equations in Fluid Mechanics, London Math. Soc. Lecture Note Ser., 452, Cambridge Univ. Press, 2018 (DOI,PDF),

• The Lagrange multiplier and the stationary Stokes equations, J. Appl. Anal. 23(2), pp. 137-140, 2017 (DOI,PDF),

• A generalised comparison principle for the Monge-Ampère equation and the pressure in 2D fluid flows, C. R. Math. Acad. Sci. Paris 356(2), pp. 198-206, 2018 (DOI,PDF),

• (with K. Chełmiński) Partial differential equations (PL: Równania różniczkowe cząstkowe), Warsaw University of Technology Publishing House, ISBN 978-83-7814-405-2, 2015, Link (PL).

Invited talks:

• Conference on ``Recent Trends in the Mathematics of Fluid Dynamics'', ICMAT-CUNEF, Madrid, Dec 2025,

• Conference on ``Advances in Mathematical Fluid Dynamics", Peking University, Jun 2025,

• Analysis Seminar, Basel University, Apr 2025,

• Analysis and PDE seminar, UCLA, Los Angeles, Feb 2025,

• Analysis seminar, Yonsei University, Seoul, Dec 2024,

• Special Session ``Recent advances in mathematical fluid dynamics'', Joint meeting of the NZMS, AustMS and AMS, Auckland, Dec 2024,

• Fluids seminar, Princeton University, Princeton, Nov  2024,

• Analysis Seminar, University of Southern California, Nov 2024,

• Analysis and PDE seminar, Caltech, Pasadena, Oct 2024,

• PDE and Applied Math seminar, University of Maryland, College Park, Oct 2024,

• Special Session ``Recent Advances in Fluid mechanics: Theory and Computation'', 2nd AMS-UMI International Joint Meeting, Palermo, Jul 2024,

• Second Joint Alabama-Florida Conference on Differential Equations, Dynamical Systems and Applications, Tallahassee, May 2024,

• PDE Seminar, North Carolina State University, Mar 2024,

• Applied Math and Analysis Seminar, Duke University, Mar 2024,

• Special Session on ``Fluids: Analysis, Applications, and Beyond'', AMS Spring Southeastern Sectional Meeting, Tallahassee, Mar 2024,

• Applied Mathematics Seminar, University of Victoria, Feb 2024,

• Applied and Computational Mathematics Seminar, Florida State University, Jan 2024,

• ``Fluids in Seoul 2024'', Seoul, Jan 2024,

• Open PDE Seminar, Warsaw University of Technology, Dec 2023, 

• PDE Seminar, Institute of Mathematics of Polish Academy of Sciences, Warsaw, Poland, Dec 2023,

• PDE Seminar, Chinese Academy of Sciences, Dec 2023,

• The 41st Southeastern-Atlantic Regional Conference on Differential Equations, Florida A&M University, Tallahassee, Nov 2023,

• PDE Seminar, Florida State University, Nov 2023,

• Fluid Dynamics 2 Reunion Seminar, SLMath (MSRI), Berkeley, Jul 2023,

• PDE Seminar, Purdue University, Apr 2023,

• Applied and Computational Mathematics Seminar, Florida State University, Apr 2023,

• Applied Math and Analysis Seminar, Duke University, Mar 2023, 

• Special Session on Dynamics of Partial Differential Equations, AMS Spring Southeastern Sectional Meeting, Georgia Tech, Mar 2023, 

• CAMS Colloquium, University of Southern California, Mar 2023, 

• PDE Seminar, Seoul National University, Feb 2023, 

• PDEs and Fluid Mechanics Seminar, ICMAT, Madrid, Dec 2022, 

• MathFlows conference, CIRM, Marseilles, France, Dec 2022, 

• Analysis Seminar, University of British Columbia, Nov 2022,

• USC Analysis Seminar, Oct 2022,

• UCLA Analysis and PDE Seminar, Oct 2022,

• Applied and Computational Mathematics Seminar, Florida State University, Oct 2022,

• PDE Seminar, Seoul National University, Aug 2022,

• PDEs and Fluid Mechanics Seminar, ICMAT, Madrid, Jun 2022,

• The AIM workshop “Criticality and stochasticity in quasilinear fluid systems”, San Jose, May 2022,

• Colloquium, Florida State University, Feb 2022,

• Colloquium, University of North Texas, Feb 2022,

• Analysis Seminar, Florida Institute of Technology, Feb 2022,

• Colloquium, University of Hawaii at Manoa, Feb 2022,

• Colloquium, Georgia Tech, Jan 2022,

• Colloquium, The Chinese University of Hong Kong, Jan 2022,

• 2021 Winter Young Mathematician Forum, Shanghai Jiao Tong University, Dec 2021,

• PDE and Applied Mathematics Seminar, University of California, Riverside, Dec 2021,

• Colloquium, Texas Tech University, Nov 2021,

• Colloquium, Southern University of Science and Technology, Shenzhen, Nov 2021,

• Nonlinear PDE Seminar, University of Wisconsin-Madison, Oct 2021,

• Post-pandemic Analysis workshop, Będlewo, Poland, Jul 2021,

• Special Session on Regularity Theory for Linear and Nonlinear PDEs, AMS Spring Western Sectional Meeting, May 2021,

• Analysis and Applied Mathematics Seminar, University of Illinois at Chicago, Jan 2021,

• Open PDE Seminar, Warsaw University of Technology, Nov 2020,

• Analysis Seminar, Beijing Normal University, Nov 2020,

• Analysis Seminar, Institute for Advanced Study, Princeton, Jan 2020,

• SIAM Conference on Analysis of Partial Differential Equations, La Quinta, Dec 2019,

• Special Session on Fluid Dynamics: from Theory to Numerics, AMS Fall Western Sectional Meeting, University of California, Riverside, Nov 2019,

• CAMS Colloquium, University of Southern California, Oct 2019,

• Analysis Seminar, University of Southern California, Sep 2019,

• Summer School in Mathematical Fluid Mechanics, Cetraro (Italy), Jun 2019,

• Analysis Seminar, Courant Institute of Mathematical Sciences, New York University, Feb 2019,

• Optimal Transport Theory and Hydrodynamics, Oberwolfach Seminar, Germany, Oct 2018,

• Navier–Stokes seminar, University of Oxford, May 2018,

• Workshop on Mathematical Fluid Mechanics, Bad Boll (Germany), May 2018,

• Nonlinear Differential Equations with Applications in Continuum Mechanics (dedicated to Professor Krzysztof Chełmiński on the occasion of the jubilee of his 60th birthday), Warsaw University of Technology, Mar 2018,

• Analysis seminar, University of Leipzig, Feb 2018,

• postgraduate seminar, University of Warwick, Dec 2017,

• Open PDE seminar, Warsaw University of Technology, Nov 2017,

• Interdisciplinary Research Workshop, Będlewo (Poland), May 2017,

• postgraduate seminar, University of Warwick, Jan 2017,

• Analysis and PDEs Seminar, University of Sussex, Nov 2016,

• Young Researchers in Mathematics 2016, University of St Andrews, Aug 2016,

• MASDOC Retreat, Longville in the Dale, May 2016,

• CCA-MASDOC-OxPDE workshop, University of Cambridge, Mar 2016,

• postgraduate seminar, University of Warwick, Oct 2015,

• Open PDE seminar, Warsaw University of Technology, Apr 2015

Some short mathematical notes:

• An introduction to convex integration (PDF)

• The Fatou lemma and Dominated and Monotone convergence theorems are equivalent to each other (PDF) 

Some of my nonmathematical work: Photo gallery, Youtube channel