Last Date: Sunday, December 15, 2024

Supervisors: Dr Matthew Schrecker, Prof Manuel Del Pino

Competition Funded PhD Project (Students Worldwide)

University of Bath    Department of Mathematical Sciences

About the Project

This project is one of a number that are in competition for funding from the University of Bath URSA competition, for entry in September 2025.

Overview of the Research:

This project will address problems in the research field of mathematical analysis and the theory of nonlinear PDE.

The classical description of a star is as a self-gravitating fluid, coupling the equations of gas dynamics to a gravitational force induced by the matter. The solutions to these partial differential equations exhibit a fascinating array of behaviour, including the formation of singularities through the collapse of stars under their own gravity. This process of collapse is fundamental for understanding both the birth and death of stars, but has proved challenging for rigorous mathematical analysis due to the nonlinearity of the equations involved.

The aim of the project is to study in detail some particularly important model singularities. Recent progress in the study of these problems has led both to significant new mathematical results and the development of new tools in analysis to study singularities for quasilinear problems. The main goals for the project include the rigorous proof of existence of the singular solutions and to establish their stability and instability properties.

Advanced training in these areas is offered through courses and seminars such as the Taught Course Centre and Analysis Seminar. There is also the possibility of participating in the activities of the doctoral training centre in ‘Statistical and Applied Mathematics in Bath’ (SAMBa), whose remit includes Applied Analysis.

The Department of Mathematical Sciences at the University of Bath is an ideal environment to pursue such a project. It is home not only to experts in PDEs, but also to experts in pure and applied aspects of fluid mechanics.

Project keywords: analysis of PDE; nonlinear partial differential equations; gas dynamics; dynamical systems; functional analysis

Candidate Requirements:

Applicants should hold, or expect to receive, a First Class or good Upper Second Class UK Honours degree (or the equivalent) in a relevant subject. A master’s level qualification would also be advantageous.

Non-UK applicants must meet the programme’s English language requirement by the application deadline.

Enquiries and Applications:

Informal enquiries to Dr Matthew Schrecker, mris21@bath.ac.uk are welcome.

Formal applications should be submitted via the University of Bath’s online application form for a PhD in Mathematics prior to the closing date of this advert.

IMPORTANT:

When completing the application form:

1.      In the Funding your studies section, select ‘University of Bath URSA’ as the studentship for which you are applying.

2.      In the Your PhD project section, quote the project title of this project and the name of the lead supervisor in the appropriate boxes.

Failure to complete these two steps will cause delays in processing your application and may cause you to miss the deadline.

More information about applying for a PhD at Bath may be found on our website.

Equality, Diversity and Inclusion:

We value a diverse research environment and aim to be an inclusive university, where difference is celebrated and respected. We welcome and encourage applications from under-represented groups.

If you have circumstances that you feel we should be aware of that have affected your educational attainment, then please feel free to tell us about it in your application form. The best way to do this is a short paragraph at the end of your personal statement.

Funding Notes

Candidates may be considered for a University of Bath studentship tenable for 3.5 years. Funding covers tuition fees, a stipend (£19,237 p/a in 2024/5) and access to a training support budget.