HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Source-solutions for the multi-dimensional Burgers equation

Abstract : We have shown in a recent collaboration that the Cauchy problem for the multi-dimensional Burgers equation is well-posed when the initial data u(0) is taken in the Lebesgue space L 1 (R n), and more generally in L p (R n). We investigate here the situation where u(0) is a bounded measure instead, focusing on the case n = 2. This is motivated by the description of the asymptotic behaviour of solutions with integrable data, as t → +∞. MSC2010: 35F55, 35L65. Notations. We denote · p the norm in Lebesgue L p (R n). The space of bounded measure over R m is M (R m) and its norm is denoted · M. The Dirac mass at X ∈ R n is δ X or δ x=X. If ν ∈ M (R m) and µ ∈ M (R q), then ν ⊗ µ is the measure over R m+q uniquely defined by ν ⊗ µ, ψ = ν, f µ, g whenever ψ(x, y) ≡ f (x)g(y). The closed halves of the real line are denoted R + and R −. * U.M.P.A., UMR CNRS-ENSL # 5669. 46 allée d'Italie,
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-02481061
Contributor : Denis Serre Connect in order to contact the contributor
Submitted on : Monday, February 17, 2020 - 11:19:42 AM
Last modification on : Wednesday, February 19, 2020 - 1:38:00 AM
Long-term archiving on: : Monday, May 18, 2020 - 2:33:34 PM

Files

Burgers_source.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-02481061, version 1
  • ARXIV : 2002.07428

Collections

Citation

Denis Serre, Ecole Normale Supérieure de Lyon. Source-solutions for the multi-dimensional Burgers equation. 2020. ⟨ensl-02481061⟩

Share

Metrics

Record views

41

Files downloads

32