Contact:




Office:
E-mail:
Tel:
  Department of Mathematics
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
  Lecturer in Mathematics
  University of Sussex, Mathematics  

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

   



Full Curriculum Vitae (current as of September 2013)

Links to our Analysis and PDEs seminar and our departmental MASS seminar



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.

Click here as well for a summary of my research as it relates to that problem.



GRANT SUCCESS:

Click here for news of my recent EPSRC grant success through their 'First Grant' scheme.

The grant will run from August 2015 through July 2017, and will include a workshop (date TBD) on the Navier-Stokes regularity problem.

The link also provides quite a bit of background about my research in general.



PUBLICATIONS:       Preprint versions of all of the papers below are available at arXiv (and through the links below)

Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. Blow-up of critical Besov norms at a potential Navier-Stokes singularity. arXiv:1407.4156 (July 2014) and Comm. Math. Phys. (to appear).

Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. A profile decomposition approach to the Lt (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-present: Lecturer in Mathematics, Mathematics Department, University of Sussex