| Date | Speaker | Title/Abstract |
|---|---|---|
| 11 Feb | Edward Fraenkel University of Bath |
On the increase of capacity and surface area with asymmetry |
| 25 Feb | Melanie Rupflin University of Warwick |
Selfsimilar expanders of the harmonic map flow We analyse (expanding) self-similar solutions of the harmonic map heat flow in supercritical dimensions with respect to the questions of existence, uniqueness and stability in suitably symmetric settings. We prove that while for certain settings, there exists a unique expander to any admissible initial data, for other settings the number of self-similar solutions to the same initial data can be arbitrarily large. We show that these two cases can be distinguished by studying the energy minimising properties of the so called equator maps. |
| 9 Mar |
Carlos Mora-Corral Basque Center for Applied Mathematics |
Cavitation, distributional determinants and the regularity of inverses for elastic deformations This is a special PDE seminar taking place at 4.15 in 4W 1.7 (the Wolfson Lecture Theatre). |
| 11 Mar | Gabriel Koch University of Oxford |
Profile Decompositions, Critical Elements and Navier-Stokes We use the dispersive method of "critical elements" established by Kenig and Merle to give an alternative proof of a well-known Navier-Stokes regularity criterion due to Escauriaza, Seregin and Sverak, namely that 3-d solutions whose spatial L3-norm remain bounded in time cannot develop a singularity. The key tool is a decomposition into "profiles" of bounded sequences in critical spaces (e.g., L3). As a byproduct, we also generalize a recent result of Rusin and Sverak on "minimal blow-up data" for Navier-Stokes. This is joint work with Isabelle Gallagher and Fabrice Planchon. |
| 25 Mar | John Toland University of Bath |
Strain-Gradient Theory of Hydroelastic Travelling Waves and Young Measures of their Singular Limits |
| 8 Apr | Claudia Garetto Imperial College London |
Generalised Fourier integral operator methods for hyperbolic
equations with singular coefficients In this talk I will present some recent well-posedness results for strictly hyperbolic Cauchy problems with highly singular coefficients and initial data. These problems are in general ill-posed in the distributional setting. Solvability is obtained in a suitable framework of generalised functions (Colombeau algebras) via Fourier integral operator methods able to deal with singular phase functions and symbols. |
| 13 May | Michael Ruzhansky Imperial College London |
Operators on compact Lie groups We will review the recent work of the speaker with V. Turunen on the quantisation of operators on compact Lie groups leading to globally defined full symbols of operators. We will give several new applications of this approach to harmonic analysis and to PDEs. |
| 8 Jun | Pablo Álvarez Caudevilla University Carlos III Madrid |
The Cauchy Problem for a Fourth-Order Thin Film Equation
(4.15pm in the Wolfson Lecture Theatre) |