Morawetz inequalities
E621135
Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Morawetz inequalities canonical | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
decay estimate
ⓘ
energy estimate ⓘ mathematical concept ⓘ |
| appliesTo |
Klein–Gordon equations
NERFINISHED
ⓘ
dispersive equations ⓘ nonlinear Schrödinger equations ⓘ nonlinear wave equations ⓘ wave equations ⓘ |
| area | mathematical analysis ⓘ |
| context |
dispersive PDE
ⓘ
hyperbolic equations ⓘ scattering for nonlinear dispersive equations ⓘ |
| developedBy | Cathleen Synge Morawetz NERFINISHED ⓘ |
| field | partial differential equations ⓘ |
| hasVariant |
interaction Morawetz inequality
ⓘ
localized Morawetz inequality ⓘ weighted Morawetz inequality ⓘ |
| historicalPeriod | second half of the 20th century ⓘ |
| implies |
integrated local energy decay
ⓘ
spacetime L^2 bounds for solutions ⓘ |
| namedAfter | Cathleen Synge Morawetz NERFINISHED ⓘ |
| purpose |
to control long-time behavior of solutions
ⓘ
to derive scattering results ⓘ to obtain spacetime integrability estimates ⓘ to prevent concentration of energy ⓘ to prove decay of local energy ⓘ |
| relatedTo |
Strichartz estimates
NERFINISHED
ⓘ
a priori estimates ⓘ dispersive estimates ⓘ energy–momentum tensor ⓘ global existence results ⓘ local energy decay ⓘ multiplier method ⓘ scattering theory ⓘ |
| requires |
conservation of energy
ⓘ
suitable multiplier vector fields ⓘ |
| subfield |
PDE theory
ⓘ
scattering theory for PDE ⓘ |
| toolFor |
analysis of obstacle scattering
ⓘ
black hole spacetime wave analysis ⓘ stability analysis of solutions ⓘ |
| typicalForm |
integral of weighted energy density bounded by initial energy
ⓘ
spacetime integral inequality ⓘ |
| typicalWeight |
distance from origin
ⓘ
radial weight function ⓘ |
| usedFor |
controlling nonlinear interaction terms
ⓘ
proving asymptotic completeness ⓘ proving global well-posedness ⓘ ruling out finite-time blow-up in certain regimes ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.