Hola,
¿eres nuevo aquí?

Regístrate gratis y conecta tu empresa con financiación pública, partners y proyectos.

Tengo cuenta

Regístrate

Ver video

ULD3DNSE

Financiado

Cerrado

Uniqueness of solutions of the three dimensional Navier Stokes equations for lar...

Uniqueness of solutions of the three dimensional Navier Stokes equations for large sets of data The three-dimensional Navier-Stokes equations are the fundamental mathematical model of fluid flow. However, currently we only know that unique solutions exist for all time for 'small' data (initial condition and forcing); for 'la... ver más

30/09/2012

UNIVERSITY OF WARW...

225K€

Presupuesto del proyecto: 225K€

Líder del proyecto

UNIVERSITY OF WARWICK No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2012-09-30 No tenemos la información de la convocatoria

0% 100% 100%

Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

1 Participantes

UNIVERSITY OF WARWICK

0.00€ | Lider

Conecta tu I+D

¿Tienes un proyecto y buscas un partner? Gracias a nuestro motor inteligente podemos recomendarte los mejores socios y ponerte en contacto con ellos. Te lo explicamos en este video

Proyectos interesantes

COMANFLO Computation and analysis of statistical solutions of fluid f... 2M€ Cerrado

CAMINFLOW Computer assisted Analysis and Applications of Moving Interf... 161K€ Cerrado

ADDECCO Adaptive Schemes for Deterministic and Stochastic Flow Probl... 1M€ Cerrado

MTM2013-44699-P ANALISIS Y ECUACIONES EN DERIVADAS PARCIALES 53K€ Cerrado

MTM2016-76072-P ANALISIS GEOMETRICO Y NUMERICO DE SISTEMAS DINAMICOS Y APLIC... 65K€ Cerrado

FIS2009-08821 ESTRUCTURAS COHERENTES Y TURBULENCIA EN DOMINIOS SIMPLES 119K€ Cerrado

Líder del proyecto

UNIVERSITY OF WARWICK No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 225K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The three-dimensional Navier-Stokes equations are the fundamental mathematical model of fluid flow. However, currently we only know that unique solutions exist for all time for 'small' data (initial condition and forcing); for 'large' data they can only be guaranteed to exist for a short time. The existence of unique smooth solutions that exist for all time for any choice of data is one of the Clay Foundation's Million Dollar Millennium Prize Problems, and is exceedingly hard. The goal of this proposal is to address the problem of uniqueness of solutions in a way that does not require a solution of this problem in full. We aim to show that the solutions are unique for certain large classes of data. More concretely, we aim to prove the following three results: (i) it is possible to verify uniqueness numerically (at least in theory) for any set of initial conditions that is bounded in H^1; (ii) for a fixed initial condition, a prevalent set of forcing functions give rise to unique solutions; and (iii) for a fixed forcing function, a dense set of complex initial conditions give rise to unique solutions. The result of (i) relies on showing that the property of uniqueness is in some sense robust, which we will prove in a way that generalises previous results obtained by the host. In (ii), "prevalence" is a probabilistic notion, introduced for various problems in dynamical systems, which means that one can describe something as happening "with probability one". It is already know that this result is true if one replaces "prevalent" by "dense", but a result valid "almost surely" will be more practically relevant. Objective (iii), density of initial conditions giving rise to unique solutions, is a high-profile problem, which we will treat using results from the statistical theory of the equations developed in the 1980s.

Conecta tu I+D

Entra hoy

¿Olvidé mi contraseña?

Financiación

Empresas

CTIs/Universidades

Proyectos

Investigadores