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Dispersive estimates for 2D-wave equations with critical potentials
We study the 2D-wave equation with a scaling-critical electromagnetic potential. This
problem is doubly critical, because of the scaling invariance of the model and the …
problem is doubly critical, because of the scaling invariance of the model and the …
Decay and Strichartz estimates in critical electromagnetic fields
We study the L 1→ L∞-decay estimates for the Klein-Gordon equation in the Aharonov-
Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation …
Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation …
Strichartz estimates and wave equation in a conic singular space
J Zhang, J Zheng - Mathematische Annalen, 2020 - Springer
Consider the metric cone X= C (Y)=(0, ∞) _r * YX= C (Y)=(0,∞) r× Y with metric g= dr^ 2+ r^
2h g= dr 2+ r 2 h where the cross section Y is a compact (n-1)(n-1)-dimensional Riemannian …
2h g= dr 2+ r 2 h where the cross section Y is a compact (n-1)(n-1)-dimensional Riemannian …
[HTML][HTML] Strichartz estimates and nonlinear wave equation on nontrap** asymptotically conic manifolds
J Zhang - Advances in Mathematics, 2015 - Elsevier
We prove the global-in-time Strichartz estimates for wave equations on the nontrap**
asymptotically conic manifolds. We obtain estimates for the full set of wave admissible …
asymptotically conic manifolds. We obtain estimates for the full set of wave admissible …
Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space
Precise dispersive estimates for the wave equation inside cylindrical convex domains
M Len - Proceedings of the American Mathematical Society, 2022 - ams.org
In this work, we establish precise local in time dispersive estimates for solutions of the model
case Dirichlet wave equation inside cylindrical convex domains $\Omega\subset\mathbb …
case Dirichlet wave equation inside cylindrical convex domains $\Omega\subset\mathbb …
Global-in-time Strichartz estimates and cubic Schr\" odinger equation in a conical singular space
J Zhang, J Zheng - arxiv preprint arxiv:1702.05813, 2017 - arxiv.org
In this paper, we study Strichartz estimates for the Schr\" odinger equation on a metric cone
$ X $, where $ X= C (Y)=(0,\infty) _r\times Y $ and the cross section $ Y $ is a $(n-1) …
$ X $, where $ X= C (Y)=(0,\infty) _r\times Y $ and the cross section $ Y $ is a $(n-1) …
The diffractive wave trace on manifolds with conic singularities
GA Ford, J Wunsch - Advances in Mathematics, 2017 - Elsevier
Let (X, g) be a compact manifold with conic singularities. Taking Δ g to be the Friedrichs
extension of the Laplace–Beltrami operator, we examine the singularities of the trace of the …
extension of the Laplace–Beltrami operator, we examine the singularities of the trace of the …
Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones
J Zhang - Journal of Functional Analysis, 2022 - Elsevier
We construct the Schwartz kernel of resolvent and spectral measure for Schrödinger
operators on the flat Euclidean cone (X, g), where X= C (S σ 1)=(0,∞)× S σ 1 is a product …
operators on the flat Euclidean cone (X, g), where X= C (S σ 1)=(0,∞)× S σ 1 is a product …