What question did this study set out to answer?

Investigate the nonlinear asymptotic stability of Couette flow and shear flows governed by the 2D Euler equations of ideal, incompressible fluid dynamics.

December 30, 2013Applied Mathematics Research eXpressOpen Access

Asymptotic Stability for the Couette Flow in the 2D Euler Equations

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Authors

JBJacob BedrossianUniversity of California, Los Angeles NMNader MasmoudiNew York University Abu Dhabi

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Implication

Theoretical analysis demonstrates nonlinear asymptotic stability of Couette flow in two-dimensional Euler equations, indicating enstrophy transfer to small scales.

Key Points

Investigate the nonlinear asymptotic stability of Couette flow and shear flows governed by the 2D Euler equations of ideal, incompressible fluid dynamics.
Mathematical analysis and proof examining perturbations of Couette flow in a suitable regularity class.
Asymptotic characterization of fluid evolution and enstrophy mixing as time approaches infinity.
Small perturbations in a suitable regularity class converge strongly in L2 to a shear flow close to the original Couette flow.
Enstrophy mixes toward small scales through an almost linear evolution and vanishes in the weak limit as time approaches infinity.

Cite This Study

Bedrossian et al. (2013) studied this question.

synapsesocial.com/papers/6a712c6ef44fa9f079def496 https://doi.org/10.1093/amrx/abt009

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Implication

Theoretical analysis demonstrates nonlinear asymptotic stability of Couette flow in two-dimensional Euler equations, indicating enstrophy transfer to small scales.

Asymptotic Stability for the Couette Flow in the 2D Euler Equations

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Member takes

Implication

Key Points

Cite This Study

Asymptotic Stability for the Couette Flow in the 2D Euler Equations

Discussion

Member takes

Implication

Key Points

Cite This Study

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