Vlad Vicol
Vlad Cristian Vicol is a mathematician who studies Partial Differential Equations (PDE), specifically regularity problems in PDE of hydrodynamics .
Vicol studied at Jacobs University in Bremen with a bachelor's degree in 2005 on a scholarship and received his doctorate in mathematics from Igor Kukavica at the University of Southern California in 2010 ( Analyticity and Gevrey-class regularity for the Euler equations ). The dissertation dealt with the propagation of the analysis and Gevrey regularity for the Euler equation in bounded domains. As a post-doctoral student , he was a Dickson Instructor at the University of Chicago with Peter Constantin from 2010 to 2012and dealt with the global regularity of the critical SQG (surface quasi-geostrophic equation) equation for high data volumes. In 2012 he became Assistant Professor at Princeton University and in 2018 Associate Professor at the Courant Institute at New York University .
In 2017, Vicol and Tristan Buckmaster proved that there are initial conditions for which weak solutions of the Navier-Stokes equations in hydrodynamics, which are widely used, for example, in the modeling of turbulence and in fluids with friction in general, are ambiguous. This is interpreted as an indication of possibly pathological behavior of these equations or the mathematical approach to these via weak solutions, chosen since Jean Leray . The regularity behavior of the solutions to the Navier-Stokes equations is the subject of one of the Millennium Problems . In their proof, they used the methods of László Székelyhidi and Camillo De Lellis , who had previously achieved a scientific breakthrough in a hydrodynamic equation (the Euler equation) closely related to the Navier-Stokes equations (limiting case of vanishing viscosity).
He also deals with many other equations in hydrodynamics ( boundary layer equations , quasigeostrophic theory , non-local active scalar equations, etc.). With the Navier-Stokes equations, he investigated long-term behavior at high Reynolds numbers .
In 2015 he gave a plenary lecture on partial differential equations at the SIAM Congress. From 2015 to 2018 he was a Sloan Research Fellow. In 2016 he received the Junior Faculty Teaching Award in Princeton, in 2017 the Mathematical Congress of the Americas (MCA) Prize in Montreal and in 2019 the Clay Research Award with Tristan Buckmaster and Philip Isett . Buckmaster and Vicol got it for showing that weak solutions to the Navier-Stokes equation can be surprisingly wild (highly discontinuous and highly ambiguous). Isett received the award for completely solving the Onsager conjecture - Buckmaster and Vicol were previously heavily involved in this.
Fonts (selection)
- with Camillo De Lellis, László Székelyhidi Jr., Tristan Buckmaster: Onsager's conjecture for admissible weak solutions, Communications on Pure and Applied Mathematics, Volume 72, 2019, pp. 229-274, Arxiv 2017
- with Tristan Buckmaster: Nonuniqueness of weak solutions to the Navier-Stokes equation, Annals of Mathematics, Volume 189, 2019, pp. 101–144, Arxiv
- with Tristan Buckmaster, Maria Colombo: Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1, Arxiv 2018
- with Tristan Buckmaster: Convex integration and phenomenologies in turbulence, EMS Surveys in Mathematical Sciences, 2019, Arxiv 2019
Web links
Individual evidence
- ↑ Vlad Vicol in the Mathematics Genealogy Project (English)
- ^ Clay Research Award 2019
| personal data | |
|---|---|
| SURNAME | Vicol, Vlad |
| ALTERNATIVE NAMES | Vicol, Vlad Cristian |
| BRIEF DESCRIPTION | mathematician |
| DATE OF BIRTH | 20th century |