Professor James Robinson

James Robinson

Professor of Mathematics

Office: C2.20
Phone: +44 (0)24 7652 4657
Fax: +44 (0)871 256 4140
Email: J dot C dot Robinson at warwick dot ac dot uk

Teaching Responsibilities 2022/23:

Term 1: Analysis I

Term 2: MA254 Theory of ODEs

Research Interests:
Rigorous fluid dynamics and turbulence; infinite-dimensional dynamical systems; non-autonomous dynamical systems; embeddings of finite-dimensional sets into Euclidean spaces; dimension theory.

Books:

J C Robinson (2001) Infinite-dimensional dynamical systems. Cambridge University Press.

J C Robinson (2004) An introduction to ordinary differential equations. Cambridge University Press.

J C Robinson (2011) Dimensions, embeddings, and attractors. Cambridge Tracts in Mathematics 186, Cambridge University Press. Errata.

A N Carvalho, J A Langa, & J C Robinson (2012) Attractors for infinite-dimensional non-autonomous systems. Springer Applied Mathematical Sciences 182.

J C Robinson, J L Rodrigo, & W Sadowski (2016) Classical theory of the three-dimensional Navier-Stokes equations. Cambridge Studies in Advanced Mathematics 157. Cambridge University Press. Errata.

J C Robinson (2020) An introduction to functional analysis. Cambridge University Press. ErrataLink opens in a new window.

Selected papers:

C L Fefferman, K W Hajduk, & J C Robinson (2022) Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces. Proceedings of the LMS 125, 759-777.

J C Robinson (2021) Using periodic boundary conditions to approximate the Navier-Stokes equations on \({\mathbb R}^3\) and the transfer of regularity. Nonlinearity 34, 7683-7704.

J C Robinson (2020) The Navier-Stokes regularity problem. Philos. Trans. Roy. Soc. A 378, no 2174, 20190526.

R Laister, J C Robinson, M Sierzega, A Vidal-Lopez (2016) A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 33, 1519-1538.

J C Robinson & J J Sánchez-Gabites (2016) On finite-dimensional global attractors of homeomorphisms. Bull. London Math. Soc. 48, 483-498.

J M Fraser, A M Henderson, E J Olson, & J C Robinson (2015) On the Assouad dimension of self-similar sets with overlaps. Advances in Mathematics 273, 188-214.

C Fefferman, D MCormick, J C Robinson, & J L Rodrigo (2014) Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Journal of Functional Analysis 267, 1035-1056.

J C Robinson & A Vidal-López (2013) Minimal periods for semilinar parabolic equations revisited. Journal of Differential Equations 254, 4279-4289.

G Lukaszewicz, J Real, & J C Robinson (2011) Invariant measure for dissipative systems and generalised Banach limits. Journal of Dynamics and Differential Equations 23, 225-250.

E J Olson & J C Robinson (2010) Almost bi-Lipschitz embeddings and almost homogeneous sets. Transactions of the American Mathematical Society 362, 145-168.

J C Robinson & W Sadowski (2009) Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations. Nonlinearity 22, 2093-2099.

M Dashti & J C Robinson (2009) A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations. Nonlinearity 22, 735-746.

J C Robinson (2009) Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces. Nonlinearity 22, 753-746.

S I Chernyshenko, P Constantin, J C Robinson, & E S Titi (2007) A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. Journal of Mathematics Physics 48, 065204: 1-15.

A Carvalho, J A Langa, J C Robinson, & A Suárez (2007) Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Journal of Differential Equations 236, 570-603.

J C Robinson (2007) Parametrization of global attractors, experimental observations, and turbulence. Journal of Fluid Mechanics 578, 495-507.

T Carballo, H Crauel, J A Langa, & J C Robinson (2007) The effect of noise of the Chafee-Infante equation: a nonlinear case study. Proceedings of the American Mathematical Society 135, 373-382.

J A Langa, J C Robinson, & A Suárez (2006) Bifurcations in non-autonomous scalar equations. Journal of Differential Equations 221, 1-35.

J A Langa & J C Robinson (2006) Fractal dimension of a random invariant set. Journal de Mathematiquest Pure et Appliques 85, 269 -294.

J C Robinson (2005) A topological delay embedding theorem for infinite-dimensional dynamical systems. Nonlinearity 18, 2135-2143.

I Kukavica & J C Robinson (2004) Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. Physica D 196, 45-66.

T Caraballo, J A Langa, & J C Robinson (2001) A stochastic pitchfork bifurcation in a reaction-diffusion equation. Proceedings of the Royal Soceity of London Series A 457, 2041-2061.

P K Friz & J C Robinson (2001) Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite set of nodal values. Physica D 148, 201-220.

Conference proceedings:

J C Robinson & P A Glendinning (2001) From finite to infinite dimensional dynamical systems, proceedings of the NATO ASI workshop at the Isaac Newton Institute, August 1995. Kluwer Academic.

J C Robinson & J L Rodrigo (2009) Partial Differential Equations and Fluid Mechanics. LMS Lecture Notes Series. Cambridge University Press.

J C Robinson, J L Rodrigo, & W Sadowski (2012) Mathematical Aspects of Fluid Mechanics. LMS Lecture Notes Series. Cambridge University Press.

J C Robinson, J L Rodrigo, W Sadowski, & A Vidal-López (2015) Recent progress in the theory of the Euler and Navier-Stokes equations. LMS Lecture Notes Series. Cambridge University Press.

C Fefferman, J C Robinson, & J L Rodrigo (2018) Partial Differenatial Equations and Fluid Mechanics. LMS Lecture Notes Series. Cambridge University Press. In preparation.

Research grants:

EPSRC Leadership Fellowship EP/G007470/1 : The Navier-Stokes equations: functional analysis and dynamical systems (01/10/2008 - 30/4/2014)

Royal Society University Research Fellowship: Practical implications from the theory of global attractors (01/10/1999 - 30/9/2007)

Royal Society Joint Project (with Seville): Bifuration theory for non- autonomous differential equations (01/07/2002 - 30/06/2004)