Year: 2025
Type: article
Abstract: The half-wave maps equation is a nonlocal geometric equation arising in the continuum dynamics of Haldane-Shashtry and Calogero-Moser spin systems. Global wellposedness for small data in the critical space $${\dot{B}}^{n/2}_{2,1}$$ B ˙ 2 , 1 n / 2 is known since [11, 15] for dimensions $$n\geqslant 4$$ n ⩾ 4 . There is a major obstruction to extending these results to $$n=3$$ n = 3 due to the loss of the $$L^2_tL^\infty _x$$ L t 2 L x ∞ Strichartz estimate. In this work, we prove that the equation admits global solutions for small smooth data in $${\dot{B}}^{3/2}_{2,1}$$ B ˙ 2 , 1 3 / 2 which also possesses some angular regularity and weighted decay of derivatives. We use the improved Strichartz estimates of [24] to develop trilinear estimates in Strichartz spaces weighted by commuting vector fields which avoid the use of the $$L^2_tL^\infty _x$$ L t 2 L x ∞ endpoint.
Author: Katie Marsden
Institution: University of California, Los Angeles
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7114989178