Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.
Low-regularity global well-posedness for the Boltzmann equation near vacuum
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abstract
We study the Boltzmann equation near vacuum in anisotropic low-regularity Besov spaces. We establish the global existence and uniqueness of strong solutions with the critical regularity index $2/p$ for $p\in[1,\infty)$ in $\mathbb{R}^3$. The proof relies on a new bilinear estimate for the nonlinear collision operator. Combined with a div-curl type lemma we develop, this allows us to close the a priori estimates and thereby obtain global well-posedness.
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math.AP 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Low-regularity Schr\"odinger map flow on high-dimensional periodic domains
Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.