My primary research interest is in the analysis of differential equations with irregular coefficients. Increasingly, these equations are used in a wide variety of mathematical models in fields as diverse as climate modelling, medical imaging, control theory, and stem-cell research yet the mathematical theory remains insufficiently developed for the requirements of modern scientific research. To address this gap and develop a broad mathematical theory of irregular differential equations my research draws upon the following:
I am particularly interested in problems motivated by fluid dynamics.
I organise the Mathematics Research Seminar at Middlesex.
Olson, Eric J. and Robinson, James C. and Sharples, Nicholas (2016) Generalised Cantor sets and the dimension of products. Mathematical Proceedings of the Cambridge Philosophical Society , 160 (1). pp. 51-75. ISSN 0305-0041
Robinson, James and Sadowski, Witold and Sharples, Nicholas (2013) On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations. Procedia IUTAM , 7 . pp. 161-166.
Robinson, James and Sharples, Nicholas (2013) Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Journal of Differential Equations , 254 . pp. 4144-4167.
Robinson, James and Sharples, Nicholas (2012) Strict inequality in the box-counting dimension product formulas. Real Analysis Exchange , 38 (1). pp. 95-120.