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Links to our Analysis and PDEs seminar and our departmental MASS seminar
My research interests lie in the analysis of nonlinear partial differential equations.
My most recent focus has been on the
Navier-Stokes equations governing the motion of viscous, incompressible
Click here and follow the links on that page for a summary of this long-standing and interesting problem.
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).
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 verák. Liouville theorems for the Navier-Stokes equations and applications. Acta Math., 203(1):83--105, 2009.
1996-1999: B.A., Mathematics with honors, Magna Cum Laude, Brandeis University
2000-2006: Ph.D., Mathematics, University of Minnesota (advisor: Vladimír verák)
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 for Mathematics, University of Zürich
2011-present: Lecturer in Mathematics, Mathematics Department, University of Sussex