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Local well-posedness for the periodic Boltzmann equation with constant collision kernel
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Local well-posedness for the periodic Boltzmann equation with constant collision kernel
abstract
We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain $\mathbb{T}^d$, $d\geq 2$. Using the existing techniques from nonlinear dispersive PDEs, we prove the local well-posedness result in $L^{2,r}_vH^s_x$ for $s>\frac{d}{2}-\frac{1}{4}$ and $r>\frac{d}{2}$. To reach the result, the main tool we establish is the $L^4$ Strichartz estimate for solutions to the corresponding linear equation.
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Cited by 1 Pith paper
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$l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation
Applies l²-decoupling to derive Strichartz and space-time bilinear estimates that imply unconditional uniqueness for the Boltzmann equation on R^d and T^d under Maxwellian/soft potentials with angular cutoff.
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