Global existence vs Blow-up in some nonlinear PDEs arising in fluid mechanics

Projektinformationen

TRANSIC

ID Finanzhilfevereinbarung: 624450

Projekt abgeschlossen

Startdatum 1 Oktober 2014

Enddatum 30 September 2016

Finanziert unter

• Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Gesamtkosten € 166 336,20

EU-Beitrag € 166 336,20

Koordiniert durch

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Spain

Ziel

"The present project aims at studying qualitative properties of some nonlinear Partial Differential Equations arising in fluid mechanics. It is divided into 3 parts.

Part 1 and Part 2 address the study of some classes of 1D hydrodynamic models, namely, the inviscd Surface Quasi-Gesotrophic equation (SQG) and the generalized Constantin-Lax-Majda (gCLM) equation. Both models are closely related to the 3D Euler equation written in terms of the vorticity and are therefore mathematically interesting. More specifically, Part 1 is devoted to the study of particular solutions of the inviscid (SQG) equation which blow up in finite time. Those particular solutions turn out to satisfy a 1D non local equation which are a particular case of (gCLM) equation. Therefore, we focus on that 1D equation and we prove finite time blow-up by using methods coming from harmonic analysis and the so-called ""nonlocal maximal principle"" or the ""modulus of continuity method"" introduced by Kiselev, Nazarov and Volberg.

In contrast to Part 1, Part 2 is devoted to the proof of a global existence theorem for another particular case of (gCLM) equation. Unlike Part 1 where the ""modulus of continuity method"" will be used only in one step of the proof, Part 2 is completly based on the use of the ""modulus of continuity method"".

Finally, Part 3 deals with the Muskat problem which describes the interface between two fluids of different density but same viscosity. This part is centered around a global existence result due to Constantin, Cordoba, Gancedo, Strain and is based on the use of a new formulation of the Muskat problem recently obtained by Lazar."

Wissenschaftliches Gebiet

• natural sciences › mathematics › pure mathematics › mathematical analysis › differential equations › partial differential equations

Programm/Programme

• FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Thema/Themen

• FP7-PEOPLE-2013-IEF - Marie-Curie Action: "Intra-European fellowships for career development"

Aufforderung zur Vorschlagseinreichung

FP7-PEOPLE-2013-IEF
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

MC-IEF - Intra-European Fellowships (IEF)

Koordinator

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS

Kontakt Verwaltung

Ana María De La Fuente (Ms.)

• EU-Beitrag: € 166 336,20
• Adresse: CALLE SERRANO 117 ; 28006 Madrid ; Spanien
• Region: Comunidad de Madrid › Comunidad de Madrid › Madrid
• Aktivitätstyp: Research Organisations
• Gesamtkosten: Keine Daten