Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • On application of kinetic formulation of the Le Roux system

  • Part of
  • Zhixin Cheng
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009
    Published online by Cambridge University Press:
    02 February 2009, pp. 263-272
    • Article
      • You have access
    • PDF
    • Export citation

  • We use the compensated compactness method coupled with some basic ideas of kinetic formulation developed by Lions, Perthame, Souganidis and Tadmor to give a refined proof for the existence of global bounded entropy solutions to the Le Roux system. This new method of the reduction of Young measures can be applied to solve other problems.

  • Regularity in kinetic formulations via averaging lemmas

  • Pierre-Emmanuel Jabin, Benoît Perthame
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 8 / 2002
    Published online by Cambridge University Press:
    15 August 2002, pp. 761-774
    Print publication:
    2002

  • We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity regularity for the solution to the transport equation under consideration. The method of proof is based on a decomposition of the density in Fourier space, combined with the K-method of real interpolation.