Abstract
This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L2 (ℝ). For positive times, the solution lies in L2 ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2884-2904 |
| Number of pages | 21 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 46 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jan 1 2014 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics
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Global existence of weak solutions for the burgers-hilbert equation. / Bressan, Alberto; Nguyen, Khai T.
In: SIAM Journal on Mathematical Analysis, Vol. 46, No. 4, 01.01.2014, p. 2884-2904.Research output: Contribution to journal › Article
TY - JOUR
T1 - Global existence of weak solutions for the burgers-hilbert equation
AU - Bressan, Alberto
AU - Nguyen, Khai T.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L2 (ℝ). For positive times, the solution lies in L2 ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.
AB - This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L2 (ℝ). For positive times, the solution lies in L2 ∩ L∞ . A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.
UR - http://www.scopus.com/inward/record.url?scp=84975131310&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84975131310&partnerID=8YFLogxK
U2 - 10.1137/140957536
DO - 10.1137/140957536
M3 - Article
AN - SCOPUS:84975131310
VL - 46
SP - 2884
EP - 2904
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 4
ER -