Regularity and Decay of Solutions to the Stark Evolution Equation

M. Ben-Artzi; A. Devinatz

doi:10.1006/jfan.1997.3211

Regularity and Decay of Solutions to the Stark Evolution Equation

M. Ben-Artzi^*
, A. Devinatz

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Long-time behavior and regularity are studied for solutions of the Stark equationu_t=i(-Δ-x₁+V(x))u,u(0,x)∈L ²(Rⁿ). It is shown that for a class of short-range potentialsV(x) the gain of local smoothness and the decay as t→∞ are close to those of the corresponding Schrödinger equationu_t=i(-Δ+V(x))u.

Original language	English
Pages (from-to)	501-512
Number of pages	12
Journal	Journal of Functional Analysis
Volume	154
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1997.3211
State	Published - 20 Apr 1998

Keywords

Stark Hamiltonian, global regularity, long-time decay

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10.1006/jfan.1997.3211

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AU - Devinatz, A.

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AB - Long-time behavior and regularity are studied for solutions of the Stark equationut=i(-Δ-x1+V(x))u,u(0,x)∈L 2(Rn). It is shown that for a class of short-range potentialsV(x) the gain of local smoothness and the decay as t→∞ are close to those of the corresponding Schrödinger equationut=i(-Δ+V(x))u.

KW - Stark Hamiltonian, global regularity, long-time decay

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Regularity and Decay of Solutions to the Stark Evolution Equation

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