Displaying similar documents to “A proof of the smoothing properties of the positive part of Boltzmann's kernel.”

Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.

Cédric Villani (1999)

Revista Matemática Iberoamericana

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We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L(R) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.

L-estimates for the wave equation on the Heisenberg group.

Detlef Müller, Elias M. Stein (1999)

Revista Matemática Iberoamericana

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Let £ denote the sub-Laplacian on the Heisenberg group H. We prove that e / (1 - £) extends to a bounded operator on L(H), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.

Wave equation with a concentrated moving source

Vladimír B. Kameń (1991)

Applications of Mathematics

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A tempered distribution which is an exact solution of the wave equation with a concentrated moving source on the right-hand side, is obtained in the paper by means of the Cagniard - de Hoop method.

The inviscid limit for density-dependent incompressible fluids

Raphaël Danchin (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is devoted to the study of smooth flows of density-dependent fluids in ℝ N or in the torus 𝕋 N . We aim at extending several classical results for the standard Euler or Navier-Stokes equations, to this new framework. Existence and uniqueness is stated on a time interval independent of the viscosity μ when μ goes to 0 . A blow-up criterion involving the norm of vorticity in L 1 ( 0 , T ; L ∞ ) is also proved. Besides, we show that if the density-dependent Euler equations have a smooth...