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, ...

Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates

Abstract : The Cauchy problem for a scalar conservation laws admits a unique entropy solution when the data u 0 is a bounded measurable function (Kruzhkov). The semi-group (S t) t≥0 is contracting in the L 1-distance. For the multi-dimensional Burgers equation, we show that (S t) t≥0 extends uniquely as a continuous semi-group over L p (R n) whenever 1 ≤ p < ∞, and u(t) := S t u 0 is actually an entropy solution to the Cauchy problem. When p ≤ q ≤ ∞ and t > 0, S t actually maps L p (R n) into L q (R n). These results are based upon new dispersive estimates. The ingredients are on the one hand Compensated Integrability, and on the other hand a De Giorgi-type iteration.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01858016
Contributor : Denis Serre Connect in order to contact the contributor
Submitted on : Saturday, August 18, 2018 - 10:24:07 AM
Last modification on : Tuesday, November 19, 2019 - 11:58:49 AM
Long-term archiving on: : Monday, November 19, 2018 - 12:25:28 PM

File

Burgers_DSLS.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-01858016, version 1

Collections

Citation

Denis Serre, Luis Silvestre. Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates. 2018. ⟨ensl-01858016⟩

Share

Metrics

Record views

69

Files downloads

60