Daniel Coutand

Dr

  • EH14 4AS

    United Kingdom

20082019

Research output per year

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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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Research Output

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
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  • 2 Citations (Scopus)
    52 Downloads (Pure)
    Open Access
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  • 3 Citations (Scopus)
    13 Downloads (Pure)

    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
    File
    1 Citation (Scopus)
    42 Downloads (Pure)

    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

  • 10 Citations (Scopus)

    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

  • 7 Citations (Scopus)