Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential

By Maria Pia Gualdani, Nestor Guillen. 2014

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Motivated by the question of existence of global solutions, we obtain pointwise upper bounds for radially symmetric and monotone solutions to the homogeneous Landau equation with Coulomb potential. The estimates say that blow up in the $L^\infty$-norm at a finite time $T$ can occur only if the $L^{3/2}$-norm of the solution concentrates for times close to $T$. The bounds are obtained using the comparison principle for the Landau equation and for the associated mass function. This method provides long-time existence results for the isotropic version of the Landau equation with Coulomb potential, recently introduced by Krieger and Strain.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/430a46606733e468b19584d1f254d2d1eef6110a

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In Applied Mathematics

Citations in the corpus

Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, background): “Let us also mention works studying modified Landau equations [47, 37] and the work [39] that shows that any weak radial solution to the Landau-Coulomb equation that belongs to L3/2 is automatically bounded and C2 using barrier arguments.”