Research Output per year

## 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.

## Fingerprint Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

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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Co Author Network
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## Research Output 2008 2019

- 12 Article

## 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 journal › Article

Open Access

File

Finite-time Singularities

Moving Interface

Euler

Contact

Rigid Body

## On the splash singularity for the free-surface of a Navier–Stokes fluid

Coutand, D. & Shkoller, S., 17 Jul 2018, In : Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire.Research output: Contribution to journal › Article

Navier-Stokes

Free Surface

Self-intersection

Singularity

Intersect

## 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 journal › Article

Open Access

File

## 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 journal › Article

Finite-time Singularities

Vortex Sheet

Vortex flow

Singularity

Geometry

## 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 journal › Article

Hele-Shaw Flow

Global Existence

Injection

Decay

Perturbation