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Personal profile

Research interests

My main interests are in the mathematical analysis of free boundary and interface problems arising in continuum theories. These are nonlinear partial differential equations (PDE) problems set on a unknown evolving domain moved by the unknown velocity of the fluid. They arise in different physical contexts: compressible Euler equations in gas dynamics, incompressible Euler equations in fluid dynamics, interaction between a fluid phase and an elastic body. The question of the well-posedness in Sobolev spaces for these problems is an outstanding question in PDE analysis, as geometric quantities linked to the unknown domain are here a leading order term.

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Finite-time Singularities Mathematics
Compressible Euler Equations Mathematics
Fluid Mathematics
Free Boundary Mathematics
Vortex Sheet Mathematics
Vacuum Mathematics
Singularity Mathematics
Moving Boundary Mathematics

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Research Output 2008 2019

Finite-time singularity formation for incompressible Euler moving interfaces in the plane

Coutand, D., Apr 2019, In : Archive for Rational Mechanics and Analysis. 232, 1, p. 337–387 51 p.

Research output: Contribution to journalArticle

Open Access
Finite-time Singularities
Moving Interface
Rigid Body
Free Surface

Regularity of the velocity field for Euler vortex patch evolution

Coutand, D. & Shkoller, S., May 2018, In : Transactions of the American Mathematical Society. 370, 5, p. 3689–3720 32 p.

Research output: Contribution to journalArticle

Open Access

On the Impossibility of Finite-Time Splash Singularities for Vortex Sheets

Coutand, D. & Shkoller, S., Aug 2016, In : Archive for Rational Mechanics and Analysis. 221, 2, p. 987–1033 47 p.

Research output: Contribution to journalArticle

Finite-time Singularities
Vortex Sheet
Vortex flow

Global existence and decay for solutions of the Hele-Shaw flow with injection

Cheng, C. H. A., Coutand, D. & Shkoller, S., 1 Jan 2014, In : Interfaces and Free Boundaries. 16, 3, p. 297-338 42 p.

Research output: Contribution to journalArticle

Hele-Shaw Flow
Global Existence