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# Documents  Necasova, Sarka | enregistrements trouvés : 5

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## Uniqueness of the Boussinesq system in critical spaces using maximal regularity Monniaux, Sylvie | CIRM H

Multi angle

Partial Differential Equations

We prove uniqueness of the solutions ($u$, velocity and $\theta$, temperature) of the Boussinesq system in the whole space ${\mathbb{R}}^3$ in the critical functional spaces: continuous in time with values in $L^3$ for the velocity and $L^2$ in time with values in $L^{3/2}$ in space for the temperature. The proof relies on the property of maximal regularity for the heat equation.

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## Stability of propagation fronts in congestion models Dalibard, Anne-Laure | CIRM H

Multi angle

Partial Differential Equations

The purpose of this talk is to present two 1d congestion models: a soft congestion model with a singular pressure, and a hard congestion model in which the dynamic is different in the congested and non-congested zone (incompressible vs. compressible dynamic). The hard congested model is the limit of the soft one as the parameter within the singular presure vanishes.
For each model, we prove the existence of traveling waves, and we study their stability. This is a joint work with Charlotte Perrin.
The purpose of this talk is to present two 1d congestion models: a soft congestion model with a singular pressure, and a hard congestion model in which the dynamic is different in the congested and non-congested zone (incompressible vs. compressible dynamic). The hard congested model is the limit of the soft one as the parameter within the singular presure vanishes.
For each model, we prove the existence of traveling waves, and we study their ...

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## Geometric structures in 2D Navier-Stokes flows Brandolese, Lorenzo | CIRM H

Multi angle

Partial Differential Equations

Geometric structures naturally appear in fluid motions. One of the best known examples is Saturn’s Hexagon, the huge cloud pattern at the level of Saturn’s north pole, remarkable both for the regularity of its shape and its stability during the past decades. In this paper we will address the spontaneous formation of hexagonal structures in planar viscous flows, in the classical setting of Leray’s solutions of the Navier-Stokes equations. Our analysis also makes evidence of the isotropic character of the energy density of the fluid for sufficiently localized 2D flows in the far field: it implies, in particular, that fluid particles of such flows are nowhere at rest at large distances. Geometric structures naturally appear in fluid motions. One of the best known examples is Saturn’s Hexagon, the huge cloud pattern at the level of Saturn’s north pole, remarkable both for the regularity of its shape and its stability during the past decades. In this paper we will address the spontaneous formation of hexagonal structures in planar viscous flows, in the classical setting of Leray’s solutions of the Navier-Stokes equations. Our ...

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## Compressible Euler equations under a maximal density constraint Perrin, Charlotte | CIRM H

Multi angle

In this talk, I will present recent results on solutions to a one-dimensional Euler system coupling compressible and incompressible phases. With this original fluid system we intend to model congestion (or saturation) phenomena in heterogeneous flows (mixtures, wave-structure interactions, collective motion, etc.). Here the compressible-incompressible model will be seen as the limit of a fully compressible Euler system endowed with a singular pressure law. The goal of the talk is to present theoretical results concerning this singular limit. This is a joint work with Roberta Bianchini. In this talk, I will present recent results on solutions to a one-dimensional Euler system coupling compressible and incompressible phases. With this original fluid system we intend to model congestion (or saturation) phenomena in heterogeneous flows (mixtures, wave-structure interactions, collective motion, etc.). Here the compressible-incompressible model will be seen as the limit of a fully compressible Euler system endowed with a singular ...

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## Direct methods in the theory of elliptic equations Necas, Jindrich ; Necasova, Sarka ; Simader, Christian G. | Springer 2012

Ouvrage

- xvi; 372 p.
ISBN 978-3-642-10454-1

Springer monographs in mathematics

Localisation : Ouvrage RdC (NECA)

EDP # équation elliptique # équation différencielle elliptique

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