 NSFPAR ID:
 10215542
 Date Published:
 Journal Name:
 Monthly Notices of the Royal Astronomical Society
 Volume:
 497
 Issue:
 3
 ISSN:
 00358711
 Page Range / eLocation ID:
 2670 to 2679
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract In this article, we investigate the quantitative unique continuation properties of complexvalued solutions to drift equations in the plane.We consider equations of the form Δ u + W ⋅ ∇ u = 0 {\Delta u+W\cdot\nabla u=0} in ℝ 2 {\mathbb{R}^{2}} ,where W = W 1 + i W 2 {W=W_{1}+iW_{2}} with each W j {W_{j}} being realvalued.Under the assumptions that W j ∈ L q j {W_{j}\in L^{q_{j}}} for some q 1 ∈ [ 2 , ∞ ] {q_{1}\in[2,\infty]} , q 2 ∈ ( 2 , ∞ ] {q_{2}\in(2,\infty]} and that W 2 {W_{2}} exhibits rapid decay at infinity,we prove new global unique continuation estimates.This improvement is accomplished by reducing our equations to vectorvalued Beltrami systems.Our results rely on a novel order of vanishing estimate combined with a finite iteration scheme.more » « less

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Published by the American Physical Society 2024 
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