Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.
Organisations
People |
ORCID iD |
| Gui-Qiang George Chen (Principal Investigator) |
Publications
Bae Myoungjean
(2024)
Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems
Cao G
(2023)
Minimal entropy conditions for scalar conservation laws with general convex fluxes
in Quarterly of Applied Mathematics
Chen G
(2023)
$ L^1 $-stability of vortex sheets and entropy waves in steady supersonic Euler flows over Lipschitz walls
in Discrete and Continuous Dynamical Systems
Chen G
(2021)
Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing
in Journal of Functional Analysis
Chen G
(2022)
Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
in Communications on Applied Mathematics and Computation
Chen G
(2024)
The Morawetz Problem for Supersonic Flow with Cavitation
Chen G
(2024)
Global Spherically Symmetric Solutions of the Multidimensional Full Compressible Navier-Stokes Equations with Large Data
in Archive for Rational Mechanics and Analysis
Chen G
(2024)
Hypersonic similarity for steady compressible full Euler flows over two-dimensional Lipschitz wedges
in Advances in Mathematics
Chen G
(2023)
Global solutions of the compressible Euler-Poisson equations with large initial data of spherical symmetry
in Communications on Pure and Applied Mathematics
| Description | We have successfully organised two Network Workshops and one jointly Oxbridge PDE Conference, and achieved the orginal research objectives on the generalised and low-regularity solutions of Nonlinear PDEs. |
| Exploitation Route | We envisage our research outcomes will be taken forward by the professional practiioners. |
| Sectors | Aerospace Defence and Marine Education Energy Environment |
| URL | https://www.maths.ox.ac.uk/groups/oxpde/oxpde-events |
| Description | Discontinuities and Singularities in Nonlinear Evolution PDEs, 7-8 October 2024, Oxford |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Professional Practitioners |
| Results and Impact | This workshop focuses mainly on the Analysis of Nonlinear PDEs arising in the interplay of interacting particle systems, calculus of variations, and fluid dynamics. There will be a programme of research talks, but also plenty of time to network. This event is part of the UK National PDE Network events funded by the EPSRC grant "Generalised and low-regularity solutions of nonlinear PDEs" (EPSRC EP/V008854/1), as well as the EPSRC-NSF grant "DMS-EPSRC: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications" (EPSRC-NSF EP/V051121/1). |
| Year(s) Of Engagement Activity | 2024 |
| URL | https://www.maths.ox.ac.uk/groups/oxpde/oxpde-events/discontinuities-and-singularities-nonlinear-evo... |
| Description | National PDE Network Meeting: Nonlinear PDEs of Mixed Type in Geometry and Mechanics, joint with the 13th Oxbridge PDE Conference |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This national UK PDE Network meeting (18 - 21 March 2024) for UK network members focuses on the Analysis of Nonlinear PDEs of Mixed-Type (esp. Elliptic-Hyperbolic and Hyperbolic-Parabolic Mixed PDEs) and related topics in Geometry and Mechanics. There will be a programme of research talks, but also plenty of time to network. There will be two days of talks of interest to everybody in the UK National PDE network (linked to the theme of the meeting), as well as two short courses pitched to PhD students and young researchers, and we expect that the vast majority of members will attend this part. This will be followed by a somewhat more specialised programme for people with a specific interest in the topic. We are planning to have a joint one-day programme on Thursday 21 March, joining forces with OxPDE centre members, and Cambridge PDE group members for the 13th Oxbridge PDE Conference (March 21-22 2024). |
| Year(s) Of Engagement Activity | 2024 |
| URL | https://www.maths.ox.ac.uk/groups/oxpde/oxpde-events/2024-uk-pde-network-meeting-nonlinear-pdes-mixe... |
| Description | Oxbridge PDE Conference, March 23-24, 2025 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Professional Practitioners |
| Results and Impact | This conference was held in Cambridge, and is focused on analysis and PDEs. Academics and PhD students from the two universities, together with external speakers at the Newtork Programme, were invited to give talks and/or participate. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://www.dpmms.cam.ac.uk/oxbridge-pde-conference-2023-0 |
| Description | PDE Workshop in Stability Analysis for Nonlinear PDEs, Monday 15th - Friday 19th August 2022 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | We brought together leading experts in the stability analysis of nonlinear partial differential equations across multi-scale applications. Some of the topics to be addressed include: Stability analysis of shock wave patterns of reflections/diffraction. Stability analysis of vortex sheets, contact discontinuities, and other characteristic discontinuities for multidimensional hyperbolic systems of conservation laws. Stability analysis of particle to continuum limits including the quantifying asymptotic/mean-field/large-time limits for pairwise interactions and particle limits for general interactions among multi-agent systems Stability analysis of asymptotic limits with emphasis on the vanishing viscosity limit of solutions from multidimensional compressible viscous to inviscid flows with large initial data. |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://www.maths.ox.ac.uk/node/60407 |
| Description | Workshop on Nonlinear PDEs: Stability Analysis and Multiscale Applications, April 21-23, 2023, University of Pittsburgh, USA |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This workshop is part of a series organized through a collaborative research project, a joint NSF-ESRC grant. The goal is to help develop innovative mathematical methods and techniques to solve some outstanding stability problems of nonlinear partial differential equations across the scales, including asymptotic, quantifying, and structural stability problems in hyperbolic conservation laws, kinetic equations, and related multiscale applications in fluid-particle (agent based) models. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://sites.pitt.edu/~dhwang/pde2023.html |
| Description | Workshop on Stability Analysis for Nonlinear PDEs and Multiscale Applications, NOvember 1-3, 2024, University of Wisconsin-Madison, USA |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This workshop is part of a series organized through a collaborative research project, a joint NSF-ESRC grant. The goal is to help develop innovative mathematical methods and techniques to solve some outstanding stability problems of nonlinear partial differential equations across the scales, including asymptotic, quantifying, and structural stability problems in hyperbolic conservation laws, kinetic equations, and related multiscale applications in fluid-particle (agent based) models. |
| Year(s) Of Engagement Activity | 2024 |
| URL | https://sites.pitt.edu/~dhwang/NSF-EPSRC.html |
| Description | Workshop on Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications, October 16-18, 2023, Penn Sate University, USA |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This workshop is part of a series organized through a collaborative research project, a joint NSF-ESRC grant. The goal is to help develop innovative mathematical methods and techniques to solve some outstanding stability problems of nonlinear partial differential equations across the scales, including asymptotic, quantifying, and structural stability problems in hyperbolic conservation laws, kinetic equations, and related multiscale applications in fluid-particle (agent based) models. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://sites.psu.edu/jabinstability/home/ |
| Description | Workshop on Stability and Multi-Scale Analysis for PDEs, May 13-15, 2024, UNiversity of Texas at Austin, USA |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This workshop is part of a series organized through a collaborative research project, a joint NSF-ESRC grant. The goal is to help develop innovative mathematical methods and techniques to solve some outstanding stability problems of nonlinear partial differential equations across the scales, including asymptotic, quantifying, and structural stability problems in hyperbolic conservation laws, kinetic equations, and related multiscale applications in fluid-particle (agent based) models. |
| Year(s) Of Engagement Activity | 2024 |
| URL | https://sites.pitt.edu/~dhwang/NSF-EPSRC.html |