Thu, 22 Jan 2026

12:00 - 13:00
C5

On a 1D Navier–Stokes model for dynamic combustion: characterisation for the depletion of reactant and global wellposedness

Siran Li
(Shanghai Jiao Tong University)
Abstract

We consider a one-dimensional compressible Navier-Stokes model for reacting gas mixtures with the same γ-law in dynamic combustion. The unknowns of the PDE system consist of the inverse density, velocity, temperature, and mass fraction of the reactant (Z). First, we show that the graph of Z cannot form cusps or corners near the points where the reactant in the combustion process is completely depleted at any time, based on a Bernis-type inequality by M. Winkler (2012) and the recent works by T. Cieślak et al (2023). In addition, we establish the global well-posedness theory of small BV weak solutions for initial data that are small perturbations around the constant equilibrium state (1, 0, 1, 0) in the L1(R)∩BV(R)-norm, via an analysis of the Green's function of the linearised system. The large-time behaviour of the global BV weak solutions is also characterised. This is motivated by and extends the recent global well-posedness theory for BV weak solutions to the one-dimensional isentropic Navier-Stokes and Navier-Stokes-Fourier systems developed by T. Liu and S.-H. Yu (2022).

*Joint with Prof. Haitao Wang and Miss Jianing Yang (SJTU)

Thu, 19 Feb 2026
16:00
Lecture Room 4

Local-global compatibility at p=l beyond the self-dual case

Bence Hevesi
(University of Cambridge (DPMMS))
Abstract
Verifying local–global compatibility for automorphic Galois representations is a cornerstone of the reciprocity conjectures of Langlands, Fontaine--Mazur and Clozel and has many applications within the Langlands programme. The celebrated work of Harris–Lan–Taylor–Thorne and Scholze on attaching $\ell$-adic Galois representations to cohomological automorphic representations of $\mathrm{GL}_n$​ over CM fields makes it possible to address the problem beyond the self-dual case.
 
Starting with the breakthrough work of Allen–Calegari–Caraiani–Gee–Helm–Le Hung–Newton–Scholze–Taylor–Thorne, it is now known that local–global compatibility (up to semisimplification) holds in this level of generality under irreducibility and genericity assumptions on the residual representation. In this talk, I will discuss work on removing both of these assumptions, as well as an application to the vanishing of adjoint Bloch–Kato Selmer groups, generalising work of Newton–Thorne and A’Campo. This is joint work in progress with Lambert A’Campo, Jack Thorne, and Dmitri Whitmore.
On the Dehn functions of central products of nilpotent groups
 García-Mejía, J Llosa Isenrich, C Pallier, G Transactions of the American Mathematical Society (14 Jan 2026)
A Refined Graph Container Lemma and Applications to the Hard‐Core Model on Bipartite Expanders
 Jenssen, M Malekshahian, A Park, J Random Structures and Algorithms volume 68 issue 1 (12 Jan 2026)
On the paper “Bundle gerbes” by Michael Murray
 Hitchin, N Journal of the London Mathematical Society volume 113 issue 1 (01 Jan 2026)

Meet the Head of Division

Professor James Naismith, Head of the Mathematical, Physical and Life Sciences division here in Oxford will be joining our coffee morning in the Common Room on Monday 26 January from 11 am.

Please do join Jim for coffee if you can.

Poster

IMA Events

The Institute of Mathematics and its Applications (IMA) runs a range of events including  conferences on topics ranging from cryptography to mathematics anxiety.

Check them out.

Exponential distillation of dominant eigenproperties
 Bakó, B Araki, T Koczor, B PRX Quantum
Subscribe to