Smoothing Effects for Classical Solutions of the Full Landau Equation
By Yemin Chen, Laurent Desvillettes, Lingbing He. 2009
69 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/43138601ce072971a9ef468b359ca4581097abec
How researchers see this paper
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In Applied Mathematics
- C. Imbert
- Luis Silvestre
- Clément Mouhot
- Philip T. Gressman
- Robert M. Strain
- Tong Yang
- S. Ukai
- Chao-Jiang Xu
In Mathematical Physics
- C. Imbert
- Robert M. Strain
- Philip T. Gressman
- Clément Mouhot
- Tong Yang
- S. Ukai
- Chao-Jiang Xu
- Yoshinori Morimoto
Citations in the corpus
- Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation (2009, result): “For the spatially inhomogeneous problem, a regularizing result was obtained in [ 20 ], where the H 8 regularity is”
- Enhanced Dissipation, Hypoellipticity, and Anomalous Small Noise Inviscid Limits in Shear Flows (2015, methodology): “Finally, we remark that Gevrey class hypoelliptic smoothing has been identified in the Prandtl equations [37] and in collisional kinetic theory for the Boltzmann (without angular cut-off) [2] and the Landau-Fokker-Planck equations [14].”
- Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, background): “…equation has been investigated so far in two different settings: either for weak spatially homogeneous solutions (non-negative in L 1 and with finite energy) [6, 20, 59, 22] (see also the related entropy dissipation estimates in [23, 21]), or for classical spatially heterogeneous solutions [14, 50].”
- Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, methodology): “For the study of the regularizing effect, one of the main difficulties comes from the coupling of the transport operator with the collision operator, which is similar to the Landau equation studied in [ 25 ].”
- Global classical solutions of the Boltzmann equation without angular cut-off (2009, background): “It would also be interesting to prove the instantaneous C regularizing effect for our solutions in the spirit of [17].”