# Dr Wojciech Ożański

## Wojciech OżańskiResearch Fellow |

Postdoctoral Fellow in the group of José Rodrigo.

**Interests:** the Navier-Stokes equations, Harmonic Analysis, Functional Analysis, Nonlinear Elliptic PDEs.

**Education:**

University of Warwick, MASDOC program (SRP dissertation, PhD thesis)

University of Oxford, MSc in Mathematical Modelling and Scientific Computing (MSc dissertation)

Warsaw University of Technology, BSc in Mathematics

**Publications:**

*Weak solutions to the Navier-Stokes inequality with arbitrary energy profiles*, 2018, to appear in(PDF),*Comm. Math. Phys.**A sufficient integral condition for local regularity of solutions to the surface growth model*,276(10), pp. 2990-3013, 2019 (DOI,PDF),*J. Funct. Anal.*- (with J. Robinson)
*Partial regularity for a surface growth model*,51(1), pp. 228-255, 2019 (DOI,PDF),*SIAM J. Math. Anal.* *The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness,*Birkhäuser/Springer, forthcoming, 2019; a preprint of the “sharpness part” is available at arXiv:1709.00602 (PDF),**Lect. Notes Math. Fluid Mech.**,- (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,, London Math. Soc. Lecture Note Ser., 452, Cambridge Univ. Press, 2018 (PDF),*Partial Differential Equations in Fluid Mechanics* *The Lagrange multiplier and the stationary Stokes equations*,23(2), pp. 137-140, 2017 (DOI,PDF),**J. Appl. Anal.***A generalised comparison principle for the Monge-Ampère equation and the pressure in 2D fluid flows*,356(2), pp. 198-206, 2018 (DOI,PDF),**C. R. Math. Acad. Sci. Paris**- (with K. Chelminski)
*Partial differential equations*(PL:*Równania różniczkowe cząstkowe*), Warsaw University of Technology Publishing House, ISBN 978-83-7814-405-2, 2015, Link (PL), Contents (PL/EN).

**Talks (and poster presentations):**

*Weak solutions to the Navier–Stokes inequality with arbitrary energy profiles*, Analysis Seminar, New York University, 28th Feb 2019 (abstract, slides),*A generalised comparison principle for the Monge–Ampère equation and the pressure in 2D fluid flows*, Optimal Transport Theory and Hydrodynamics, Oberwolfach Seminar, Germany, 15th Oct 2018 (abstract),- (poster)
*Partial regularity for a surface growth model*, Waves in Flows - Summer School and Workshop, Prague, 27-31 Aug 2018 (pdf), *Weak solutions to the Navier-Stokes inequality with internal singularities*, Navier-Stokes seminar, University of Oxford, 30th May 2018 (slides),*Singularities in models of fluid mechanics*, Workshop on Mathematical Fluid Mechanics, Bad Boll (Germany), 10th May 2018 (abstract, slides),*Partial regularity for the incompressible Navier-Stokes equations with counterexamples*, Nonlinear Differential Equations with Applications in Continuum Mechanics (dedicated to Professor Krzysztof Chełmiński on the occasion of the jubilee on his 60th birthday), Warsaw University of Technology, 1st Mar 2018 (slides),*Partial regularity for a surface growth model*, Analysis seminar, University of Leipzig, 1st Feb 2018 (abstract),*An invitation to convex integration*, postgraduate seminar, University of Warwick, 6th Dec 2017 (abstract),*Partial regularity for a surface growth model*, Open PDE seminar, Warsaw University of Technology, 16th Nov 2017 (abstract (PL)),- (poster)
*Partial regularity for a surface growth model*, A Sussex School and Workshop on the Navier-Stokes and Euler Equations, Brighton, 18-22 Sep 2017 (pdf), *Partial regularity of the three-dimensional Navier-Stokes equations and of a related one-dimensional surface growth model*, Interdisciplinary Research Workshop, Będlewo, 13th May 2017 (abstract (PL)),*How to construct a solution to the Navier-Stokes inequality that blows up*, postgraduate seminar, University of Warwick, 25th Jan 2017 (abstract),*Weak solutions to the Navier-Stokes inequality with internal singularities*, Analysis and PDEs Seminar, University of Sussex, 28th Nov 2016 (abstract),- (poster)
*Weak solutions to the Navier-Stokes inequality with internal singularities*, EPSRC Symposium: PDEs in Fluid Mechanics, 26-30 Sep 2016 (pdf), *Singularities in the 3D incompressible Navier-Stokes equations*, YRM 2016, University of St Andrews, 2nd Aug 2016 (abstract, slides),*The local energy inequality and the partial regularity results for the 3D incompressible Navier-Stokes equations*, MASDOC Retreat, Longville in the Dale, 24th May 2016 (abstract, slides),*The dimension of singular sets in the 3D incompressible Navier-Stokes equations and in a related 1D surface growth model*, CCA-MASDOC-OxPDE workshop, University of Cambridge, 18th Mar 2016 (abstract, slides),*The Monge–Ampère equation with application to the 2D incompressible Navier-Stokes equations*, postgraduate seminar, University of Warwick, 14th Oct 2015 (abstract),*Analysis and approximation of a strain-limiting nonlinear elastic model*(PL), Open PDE seminar, Warsaw University of Technology, 9th Apr 2015 (abstract (PL), slides (PL)).

**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),

**I am grateful for the received financial support:**

EPSRC Scholarship within MASDOC (Oct 2014 - Jul 2018),

KAUST Scholarship at University of Oxford (Oct 2013 - Sep 2014),

EUKLA (European Korean Leadership Alliance) Studentship at Kyungpook National University, South Korea (Feb - Jul 2011),

Warsaw University of Technology Rector's Scholarship (2010/2011, 2011/2012 and 2012/2013).

**Some of my nonmathematical work:** YouTube channel, photo gallery