Professor, Mathematics Fast Track Program Director
(205) 934-2154
University Hall 4051
Research and Teaching Interests: Applied analysis and mathematical physics; nonlinear partial differential equations arising as models in incompressible fluid and plasma dynamics; mathematical theory of turbulence.
Education:
- B.S., University of Zagreb (Croatia), Applied Mathematics
- Ph.D., Indiana University (Bloomington), Mathematics
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Positions
- The University of Alabama at Birmingham, Department of Mathematics, Professor (2023-)
- University of Virginia, Department of Mathematics, Interim Chair (2017-2018)
- University of Virginia, Department of Mathematics, Professor (2012-2023)
- University of Virginia, Department of Mathematics, Associate Professor (2007-2012)
- University of Virginia, Department of Mathematics, Assistant Professor (2001-2007)
- The University of Texas at Austin, Department of Mathematics, Instructor (1998-2001)
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Visiting Positions
- Princeton University, Visiting Fellow (Spring 2017)
- The University of Chicago, Long Term Visitor (Fall 2011, Fall 2004)
- Los Alamos National Laboratory, CNLS, Visiting Scientist (Summer 1998)
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Major Research Funding
- NSF DMS - 2307657, Three problems in fluid mechanics through the lens of sparseness of the regions of intense fluid activity, 09/01/2023-08/31/2026, PI
- NSF DMS - 2009607, Toward Criticality of the Navier-Stokes Regularity Problem, 07/01/2020-06/30/2023, PI
- NSF DMS - 1515805, Turbulent Cascades and Dissipation in the 3D Navier-Stokes Model, 09/01/2015-03/31/2019, PI; collaborative research with R. Dascaliuc, Oregon State University, PI
- Lundbeckfonden R217-2016-446, Gamification of Turbulent Flow, 06/30/2016-07/01/2018, PI; collaborative research with R. Feidenhans'l, Niels Bohr Institute, PI (project manager), J. Sherson, Aarhus University, PI and R.S. Kjaergaard, Aarhus University, PI
- The Research Council of Norway, Prosjekt 213474/F20 FRINATEK (Independent basic research projects in Mathematics, Physical Science and Technology), Nonlinear PDE in Spaces of Analytic Functions, 01/01/2012-12/31/2015, PI; collaborative research with H. Kalisch, University of Bergen, PI (project manager) and S. Selberg, Norwegian University of Science and Technology, PI
- NSF DMS - 1212023, Turbulent Cascades and Regularity Theory in Physical Scales of 3D Incompressible Fluid Flows, 09/01/2012-8/31/2015, PI; collaborative research with R. Dascaliuc, Oregon State University, PI
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Major Lectures
- Recent Advances in Mathematical Fluid Dynamics, Duke (2023)
- Mathematical Aspects of Hydrodynamics, MFO, Oberwolfach, Germany (2019)
- Gran Sasso Science Institute Intensive Program on Fluids and Waves, L'Aquila, Italy (2018)
- Niels Bohr Institute, Copenhagen, Denmark (2016)
- The 11th Japanese-German International Workshop on Mathematical Fluid Dynamics, Waseda University, Tokyo, Japan (2015)
- Mathematical Analysis of Turbulence, IPAM/UCLA (2014)
- Recent Advances in PDEs and Applications, a conference in honor of Hugo Beirao da Veiga's 70th birthday, CIRM, Levico, Italy (2014)
- Recent Advances in PDEs and Fluids, Stanford (2013)
- International Winter School on Mathematical Fluid Dynamics, CIRM, Levico, Italy (2012)
- RIMS Seminar: Modern Approach and Developments to Onsager's Theory on Statistical vortices, Kyoto, Japan (2011)
- International Conference on PDEs Modeling Fluids and Complex Fluids; Celebrating the 60th Birthday of Professor Peter Constantin, Xi'an, China (2011)
- Mathematical physics and PDEs, CIRM, Levico, Italy (2009)
- Workshop on Fluids and PDE II, Instituto de Matematica-UFRJ, Rio de Janeiro, Brazil (2008)
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Selected Service to Profession
- Panelist and reviewer for NSF, Division of Mathematical Sciences
- Panelist and reviewer for NASA, Heliophysics Division
- Panelist and reviewer for DOE, Basic Plasma Science
- Mentor in Math Alliance, (2018-present)
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Selected Publications
- Space analyticity for the Navier--Stokes and related equations with initial data in L^p (with I. Kukavica), J. Funct. Anal. 152(1998) 447--466
- The geometric structure of the super-level sets and regularity for 3D Navier-Stokes equations, Indiana Univ. Math. J. 50 (2001) 1309--1317.
- On depletion of the vortex-stretching term in the 3D Navier-Stokes equations (with A. Ruzmaikina), Comm. Math. Phys. 247 (2004) 601--611.
- Algebraic lower bounds on the uniform radius of spatial analyticity for the generalized KdV equation (with J.L. Bona and H. Kalisch), Ann. Inst. Henri Poincare, Anal. Non Lineaire 22 (2005) 783--797.
- Localization and geometric depletion of vortex-stretching in the 3D NSE, Comm. Math. Phys. 290 (2009) 861--870.
- A regularity criterion for the 3D NSE in a local version of the space of functions of bounded mean oscillations (with R. Guberovic), Ann. Inst. Henri Poincare, Anal. Non Lineaire 27 (2010) 773--778.
- Energy cascades and flux locality in physical scales of the 3D NSE (with R. Dascaliuc), Comm. Math. Phys. 305 (2011) 199--220.
- Anomalous dissipation and energy cascade in 3D inviscid flows (with R. Dascaliuc), Comm. Math. Phys. 309 (2012) 757--770.
- Coherent vortex structures and 3D enstrophy cascade (with R. Dascaliuc), Comm. Math. Phys. 317 (2013) 547--561.
- A geometric measure-type regularity criterion for solutions to the 3D Navier-Stokes equations, Nonlinearity 26 (2013) 289--296.
- A spatially localized L log L estimate on the vorticity in the 3D NSE (with Z. Bradshaw), Indiana Univ. Math. J. 64 (2015) 433--440.
- Frequency localized criteria for the 3D Navier-Stokes equations (with Z. Bradshaw), Arch. Rational Mech. Anal. 224 (2017) 125--133.
- An algebraic reduction of the `scaling gap' in the Navier-Stokes regularity problem (with Z. Bradshaw and A. Farhat), Arch. Rational Mech. Anal. 231 (2018) 1983--2005.
- Local near-Beltrami structure and depletion of the nonlinearity in the 3D Navier-Stokes flows (with A. Farhat), J. Nonlinear Sci. 29 (2019) 803--812.
- Oscillations and integrability of the vorticity in the 3D NS flows (with Y. Do, A. Farhat and L. Xu), Indiana Univ. Math. J. 69 (2020) 1559--1578.
- Geometry of turbulent dissipation and the Navier-Stokes regularity problem (with J. Rafner, C. Bach, J.A. Baerentzen, B. Gervang, R. Jia, S. Leinweber, M. Misztal, and J. Sherson), Scientific Reports (2021) 11:8824.