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University of Sussex                
Pevensey Buildings, Falmer Campus
Brighton BN1 9QH

Pevensey 3, Room 5c5
g.koch "at" sussex.ac.uk
01273 873076
Gabriel S. Koch
  Senior Lecturer in Mathematics
  University of Sussex, Mathematics  

Ph.D. 2006, University of Minnesota, Mathematics
Partial Differential Equations
Ph.D. Advisor: Vladimír Šverák

   


(Somewhat outdated) Curriculum Vitae (as of September 2013).

See also:

* Brief CV (current)

* Publications

* Grant Success


RESEARCH SUMMARY:

My research interests lie in the analysis of nonlinear partial differential equations.

My most recent focus has been on the Navier-Stokes equations which describe the motion of a large class of viscous, incompressible fluids.

Click here and follow the links on that page for a summary of this long-standing and interesting problem.


GRANT SUCCESS:

EPSRC grant awarded through their 'First Grant' scheme. The grant ran from October 2015 through October 2017, and included the following workshop on the Navier-Stokes regularity problem:

School and Workshop on the Navier-Stokes and Euler Equations  (18-22 September, 2017)
Here is the official link with grant details on EPSRC's "grants on the web": GOW_Koch (does not include Sussex's contribution in the grant amount)


PUBLICATIONS:       Preprint versions of all of the papers below are available at arXiv.

Gabriel S. Koch. Partial regularity for Navier-Stokes and liquid crystals inequalities without maximum principle (Preprint, 26 Oct 2021 -- to appear in Analysis & PDE)

Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. Blow-up of critical Besov norms at a potential Navier-Stokes singularity, Comm. Math. Phys. (published online 05 March 2016).

Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. A profile decomposition approach to the L∞t (L3x) Navier-Stokes regularity criterion. Math. Ann. (published online July 2012), 355(4):1527-1559, 2013.

Hajer Bahouri, Albert Cohen and Gabriel Koch. A general wavelet-based profile decomposition in the critical embedding of function spaces. Confluentes Mathematici (CM) 3(3):387-411, 2011.

Gabriel S. Koch. Profile decompositions and applications to Navier-Stokes. In Journees "Equations aux Derivees Partielles" (Port d'Albret, 2010), Exp. No. 12, 13. 2010.

Gabriel S. Koch. Profile decompositions for critical Lebesgue and Besov space embeddings. Indiana Univ. Math. J., 59:1801--1830, 2010.

Carlos E. Kenig and Gabriel S. Koch. An alternative approach to the Navier-Stokes equations in critical spaces. Ann. I. H. Poincare -- AN, 28(2):159 -- 187, 2011.

Gabriel Koch, Nikolai Nadirashvili, Gregory A. Seregin, and Vladimír Šverák. Liouville theorems for the Navier-Stokes equations and applications. Acta Math., 203(1):83--105, 2009.


BRIEF ACADEMIC CV:

1996-1999: B.A., Mathematics with honors, Magna Cum Laude, Brandeis University

2000-2006: Ph.D., Mathematics, University of Minnesota (advisor: Vladimír Šverák)

2006-2009: L. E. Dickson Instructor, Department of Mathematics, University of Chicago (mentor: Carlos E. Kenig)

2009-2011: Postdoctoral Research Fellow, Oxford Centre for Nonlinear PDE (OxPDE), Mathematical Institute, Oxford University (mentor: Gregory Seregin)

2012 (April - December): Lecturer, Institute of Mathematics, University of Zürich

2011-2016: Lecturer in Mathematics, Department of Mathematics, University of Sussex

2016-present: Senior Lecturer in Mathematics, Department of Mathematics, University of Sussex