Courbes corde-arc et espaces de Hardy généralisés

David, Guy

doi:10.5802/aif.886

Cited by 30 publications

(20 citation statements)

References 3 publications

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“…We also observe that this statement is in the spirit of the "weak with respect to strong" stability result of Dafermos [20] for hyperbolic systems.…”

Section: More Precisely If W Is a Classical Solution And U Is A Dissmentioning

confidence: 64%

“…(20) or (21) this antisymmetric part, i.e. ω, can be replaced by the symmetric part of the deformation tensor…”

Section: Remark 21mentioning

confidence: 99%

“…The hypothesis C α loc (R t ; C 1+β loc (R λ )) is replaced by H 1 loc (R t × R λ ) . The estimates are done by explicitly using theorems of G. David [20] saying that for all chord arc curves Γ : s → ξ(s), parameterized by their arc length, the Cauchy integral operator…”

Section: Analyticity and Pathologic Behavior After The Break Down Of mentioning

confidence: 99%

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Euler equations for incompressible ideal fluids

Bardos¹,

Titi²

2007

Russ. Math. Surv.

128

158

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“…We also observe that this statement is in the spirit of the "weak with respect to strong" stability result of Dafermos [20] for hyperbolic systems.…”

Section: More Precisely If W Is a Classical Solution And U Is A Dissmentioning

confidence: 64%

“…(20) or (21) this antisymmetric part, i.e. ω, can be replaced by the symmetric part of the deformation tensor…”

Section: Remark 21mentioning

confidence: 99%

See 1 more Smart Citation

Euler equations for incompressible ideal fluids

Bardos¹,

Titi²

2007

Russ. Math. Surv.

128

158

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show abstract

“…A proof of the first statement was given in our previous paper [SW], which uses a series of results from the papers [AZ,Da2,Se]. For details, see Theorem 7.1 and its proof in [SW].…”

Section: On the Structure Of T Bmentioning

confidence: 99%

On strongly quasisymmetric homeomorphisms

Ye¹,

Hu²,

Shen³

2017

Ann. Acad. Sci. Fenn. Math.

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Abstract. This short note is a continuous work of our previous paper [SW], where we were mainly concerned with the BMO theory of the universal Teichmüller space. We will endow the BMO-Teichmüller curve T b , the VMO-Teichmüller curve T v and the BMO-Teichmüller space T b with BMO manifold structures and prove that all these three spaces T b , T v and T b are contractible. We will also introduce a (new) extended BMO-Teichmüller spaceT b and endow it with BMO manifold structures.

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“…where c 2 and c 3 depend on m, M, and F L 1 (R) ; consequently, c 2 and c 3 depend on m, M, and r ; and K 16 ,K 16 , andK 16 are independent of l. In (3.86) we used the fact thatF(lξ) =F(lξ)φ(4rlξ) and therefore…”

Section: H 1/2 Compatibility Of the Initial Datamentioning

confidence: 99%

Mathematical analysis of vortex sheets

Wu¹

2005

Comm Pure Appl Math

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We consider the motion of the interface separating two domains of the same fluid that moves with different velocities along the tangential direction of the interface. The evolution of the interface (the vortex sheet) is governed by the Birkhoff-Rott (BR) equations. We consider the question of the weakest possible assumptions such that the Birkhoff-Rott equation makes sense. This leads us to introduce chord-arc curves to this problem. We present three results. The first can be stated as the following: Assume that the Birkhoff-Rott equation has a solution in a weak sense and that the vortex strength is bounded away from 0 and ∞. Moreover, assume that the solution gives rise to a vortex sheet curve that is chord-arc. Then the curve is automatically smooth, in fact analytic, for fixed time. The second and third results demonstrate that the Birkhoff-Rott equation can be solved if and only if only half the initial data is given.

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Courbes corde-arc et espaces de Hardy généralisés

Cited by 30 publications

References 3 publications

Euler equations for incompressible ideal fluids

Euler equations for incompressible ideal fluids

On strongly quasisymmetric homeomorphisms

Mathematical analysis of vortex sheets

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