Vlasov–Poisson is locally well-posed in d≥2 for finite-mass data with weighted L^{p>d} velocity envelopes and arbitrarily small uniform velocity Hölder regularity.
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Local Well-Posedness for Vlasov--Poisson with $L^{d+}$ Initial Density and Fractional Velocity Regularity
Vlasov–Poisson is locally well-posed in d≥2 for finite-mass data with weighted L^{p>d} velocity envelopes and arbitrarily small uniform velocity Hölder regularity.