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Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials - MaRDI portal

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Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials

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Publication:6509949

arXiv2305.02861MaRDI QIDQ6509949

Author name not available (Why is that?)


Abstract: For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data with low regularity, we prove its solutions at any positive time are analytic for strong angular singularity, and in Gevrey class with optimal index for mild angular singularity. To overcome the degeneracy in the spatial variable, a family of well-chosen vector fields with time-dependent coefficients will play a crucial role, and the sharp regularization effect of weak solutions relies on a quantitative estimate on directional derivatives in these vector fields.












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