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Nonlinear dispersive partial differential equations (Pure Mathematics PhD)

  • Full or part time
  • Application Deadline
    Friday, January 31, 2020
  • Competition Funded PhD Project (UK Students Only)
    Competition Funded PhD Project (UK Students Only)

Project Description

The project is mainly about well-posedness theory (existence, uniqueness of the solution, and stability of solutions under small perturbation) and global dynamics (scattering vs blow-up) of initial value problem of dispersive equations. Among nonlinear partial differential equations (PDEs), these equations are of particular importance due to their wide applications in quantum mechanics, nonlinear optics, plasma physics, and so on. The fundamental examples of nonlinear dispersive PDEs are nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), and Korteweg de Vries equations (KdV).

The analysis of dispersive PDEs is a rapidly developing subject. Our understanding of the subject has been much advanced during the past decades. New ideas and tools, such as Strichartz estimates, Fourier restriction norm method, I-method, Morawetz estimates, and induction on energy, were proposed along the way with influence beyond the subject.

Entry requirements:

We are looking for an enthusiastic and self-motivated graduate with:
[1]. A 1st class degree in Mathematics or equivalent
[2]. A solid background in analysis;
[3]. Familiarity with partial differential equations and basic functional analysis;
[4]. Good communication skills.

Informal inquiries should be directed to Dr Yuzhao Wang, e-mail:

Funding Notes

For UK and EU candidates:

[1]. Scholarships may be available in competition with all other PhD applications;
[2]. These scholarships cover all tuition fees and a maintenance allowance of approximately £14,500;
[3]. Early application is strongly recommended;
[4]. The application procedure can be found at View Website

For Chinese candidates:

[5]. The China Scholarship Council (CSC) Scholarship: View Website
[6]. China Scholarship Council (CSC) PhD Scholarships Programme at the University of Birmingham: View Website
[7]. PhD Placements and Supervisor Mobility Grants China-UK: View Website

[8]. Interested applicants are encouraged to make an informal inquiry by emailing to Dr Yuzhao Wang.

References

[1]. F. Linares, G. Ponce, Introduction to Nonlinear Dispersive Equations, Springer, (2014).
[2]. T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, American Mathematical Society, (2006).
[3]. http://web.mat.bham.ac.uk/Y.Wang/
[5]. Birmingham Analysis Group: http://web.mat.bham.ac.uk/analysis/

Related Subjects

How good is research at University of Birmingham in Mathematical Sciences?

FTE Category A staff submitted: 40.00

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