Professor James Robinson
James RobinsonProfessor of Mathematics Office: C2.20 |
Teaching Responsibilities 2020/21:
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.
Please see the link at the top of the page for research activities, including possible PhD topics.
To submit a paper to one of the following journals, please follow the link to the journal webpage:
Dynamics of Partial Differential Equations (please submit to me directly via email)
Journal of Elliptic and Parabolic Equations (please submit to me directly via email)
Proceedings of the Edinburgh Mathematical Society (submit by email to pems@icms.org.uk)
Proceedings of the Royal Society of Edinburgh Series A (submit by email to proc.rse@icms.org.uk)
Selected papers:
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.
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.
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.
J C Robinson (2005) A topological delay embedding theorem for infinite-dimensional dynamical systems. Nonlinearity 18, 2135-2143.
J A Langa & J C Robinson (2006) Fractal dimension of a random invariant set. Journal de Mathematiquest Pure et Appliques 85, 269 -294.
J A Langa, J C Robinson, & A Suárez (2006) Bifurcations in non-autonomous scalar equations. Journal of Differential Equations 221, 1-35.
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 C Robinson (2007) Parametrization of global attractors, experimental observations, and turbulence. Journal of Fluid Mechanics 578, 495-507.
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.
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.
J C Robinson (2009) Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces. Nonlinearity 22, 753-746.
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 & W Sadowski (2009) Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations. Nonlinearity 22, 2093-2099.
E J Olson & J C Robinson (2010) Almost bi-Lipschitz embeddings and almost homogeneous sets. Transactions of the American Mathematical Society 362, 145-168.
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.
J C Robinson & A Vidal-López (2013) Minimal periods for semilinar parabolic equations revisited. Journal of Differential Equations 254, 4279-4289.
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 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.
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. Errata.
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)