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Partial differential equations of Classical Physics

I shall pursue two projects both of which belong to the fields of partial differential equations, geometric analysis and mathematical physics. The first project, ``the shock development problem", belongs also to the field of fluid... ver más

28/02/2015

ETH Zürich

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH No se ha especificado una descripción o un objeto social para esta compañía.

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2015-02-28 No tenemos la información de la convocatoria

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ETH Zürich

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Líder del proyecto

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH No se ha especificado una descripción o un objeto social para esta compañía.

Presupuesto del proyecto 1M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto I shall pursue two projects both of which belong to the fields of partial differential equations, geometric analysis and mathematical physics. The first project, ``the shock development problem", belongs also to the field of fluid dynamics and aims at a full understanding of how, in the real world of 3 spatial dimensions, hydrodynamic shocks evolve, my previous work having analyzed in detail how they form. The second project, ``the formation of electromagnetic shocks in nonlinear media" aims at establishing how electromagnetic shocks form by the focusing of incoming electromagnetic wave pulses in a nonlinear medium. The case of an isotropic nonlinear dielectric will be studied first, to be followed by the case of a general isotropic medium. The methods of geometric analysis introduced in my previous work shall be employed, in particular the ``short pulse method" introduced in my work on the formation of black holes by the focusing of incoming gravitational waves in general relativity. The application of these methods to the problem for a general isotropic medium will require the development of new geometric structures. My three Ph. D. students shall purse the following three projects, belonging also to the fields of partial differential equations, geometric analysis and mathematical physics. The first project is in nonlinear elasticity. It is the study of the equilibrium configurations, in free space, of a crystalline solid in which a continuous distribution of dislocations is present, and aims at analyzing the relationship between the dislocation distribution and the resulting internal stress field. The second is in general relativity and aims at a theoretical understanding of the phenomena discovered by M. Choptuik in his numerical study of the gravitational collapse of a self-gravitating scalar field in spherical symmetry. The third is the study of hydrodynamic shock interactions and focusing in spherical symmetry.

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