Interdisciplinary research treats singularity problems in incompressible fluids
Euler’s equations are an idealised mathematical description of how fluids move. The existence of singularities in incompressible fluids is a prominent example of how these equations seem to break down under specific circumstances. The EU-funded CAPA project will undertake interdisciplinary research to address the open and practical problems singularities cause in incompressible fluids. Researchers will use numerical analysis, computer-assisted proofs and modern methods to compute partial differential equation solutions and carry out harmonic analysis. This approach is essential for treating singularities in incompressible Euler equations and surface quasi-geostrophic equations, as well as in spectral geometry applications. CAPA's findings could lead to the development of very powerful theorems describing incompressible fluids and may solve problems that cannot be addressed currently through conventional methods.
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