On the radius of analyticity of solutions to the three-dimensional Euler equations

By Igor Kukavica, Vlad Vicol. 2008

97 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/01421bf030691aeaeb97b89ab101ded5fbd6c7a3

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Landau Damping: Paraproducts and Gevrey Regularity (2013, methodology): “Like similar terms appearing in [10,45,50], the C K term (for ‘Cauchy-Kovalevskaya’) is used to absorb the highest order terms coming from E .”
Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow (2014, background): “Bounding the nonlinear term NG requires a commutator estimate which arises since uS is divergence free, in the spirit of [41, 38].”
The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space (2010, background): “The lower bound (1) improves the rate of decay from Bardos and Benachour [3] on a bounded domain (which can be inferred to be proportional to exp ∫ t 0 ‖u(s)‖Hrds), and it matches the rate of decay we obtained in [26] on the periodic domain.”
On the stability threshold for the 3D Couette flow in Sobolev regularity (2015, background): “arity (see e.g. the Cauchy-Kowalevskaya theorems of [39, 40]). The use of dissipation-like terms that appear in L2-based inﬁnite regularity estimates goes back to [25]; see also related ideas in e.g. [35, 32, 16, 38] and the references therein. The ghost energy of Alinhac [1] for quasilinear wave eq”
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations (2013, methodology): “13), begin by integrating by parts, as in the techniques [31, 52, 47] ∫ AfA(u · ∇f)dx = −(1) 2 ∫ ∇ · u |Af |(2) dx+ ∫ Af [A(u · ∇f)− u · ∇Af ] dx.”