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)
Non-autonomous Dynamical Systems
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.
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)