An $L^2$ to $L^{\mathrm{\infty }}$ Framework for the Landau Equation

Alexandre, R., Villani, C.: On the Landau approximation in plasma physics. Ann. Inst. H. Poincaré Anal. Non Linéaire 21(1), 61–95 (2004)

Boblylev, A.V., Pulvirenti, M., Saffirio, C.: From particle systems to the Landau equation: a consistency result. Commun. Math. Phys. 319(3), 683–702 (2013)

Bobylev, A., Gamba, I., Potapenko, I.: On some properties of the Landau kinetic equation. J. Stat. Phys. 161(6), 1327–1338 (2015)

Bouchut, F.: Hypoelliptic regularity in kinetic equations. J. Math. Pures Appl. (9) 81(11), 1135–1159 (2002)

Bramanti, M., Cerutti, M.C., Manfredini, M.: ${\mathcal{L}}^p$ estimates for some ultraparabolic operators with discontinuous coefficients. J. Math. Anal. Appl. 200(2), 332–354 (1996)

Carrapatoso, K., Tristani, I., Wu, K.-C.: Cauchy problem and exponential stability for the inhomogeneous Landau equation. Arch. Ration. Mech. Anal. 221(1), 363–418 (2016)

Chen, Y., Desvillettes, L., He, L.: Smoothing effects for classical solutions of the full Landau equation. Arch. Ration. Mech. Anal. 193(1), 21–55 (2009)

Desvillettes, L.: Entropy dissipation estimates for the Landau equation in the Coulomb case and applications. J. Funct. Anal. 269(5), 1359–1403 (2015)

Esposito, R., Guo, Y., Kim, C., Marra, R.: Non-isothermal boundary in the Boltzmann theory and Fourier law. Commun. Math. Phys. 323(1), 177–239 (2013)

Golse, F., Imbert, C., Mouhot, C., Vasseur, A.: Harnack inequality for kinetic Fokker–Planck equations with rough coefficients and application to the Landau equation. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19(1), 253–295 (2019)

Gressman, P.T., Strain, R.M.: Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production. Adv. Math. 227(6), 2349–2384 (2011)

Guo, Y.: The Landau equation in a periodic box. Commun. Math. Phys. 231(3), 391–434 (2002)

Guo, Y.: Decay and continuity of the Boltzmann equation in bounded domains. Arch. Ration. Mech. Anal. 197(3), 713–809 (2010)

Ha, S.-Y., Xiao, Q.: $L^2$-stability of the Landau equation near global Maxwellians. J. Math. Phys. 56(8), 081505 (2015)

Hérau, F., Pravda-Starov, K.: Anisotropic hypoelliptic estimates for Landau-type operators. J. Math. Pures Appl. (9) 95(5), 513–552 (2011)

Hérau, F., Li, W.-X.: Global hypoelliptic estimates for Landau-type operators with external potential. Kyoto J. Math. 53(3), 533–565 (2013)

Hwang, H.J., Jang, J., Jung, J.: On the kinetic Fokker–Planck equation in a half-space with absorbing barriers. Indiana Univ. Math. J. 64(6), 1767–1804 (2015)

Hwang, H.J., Jang, J., Velázquez, J.J.L.: The Fokker–Planck equation with absorbing boundary conditions. Arch. Ration. Mech. Anal. 214(1), 183–233 (2014)

Krieger, J., Strain, R.M.: Global solutions to a non-local diffusion equation with quadratic non-linearity. Commun. Partial Differ. Equ. 37(4), 647–689 (2012)

Liu, S., Ma, X.: Regularizing effects for the classical solutions to the Landau equation in the whole space. J. Math. Anal. Appl. 417(1), 123–143 (2014)

Luo, L., Yu, H.: Spectrum analysis of the linearized relativistic Landau equation. J. Stat. Phys. 163(4), 914–935 (2016)

Polidoro, S., Ragusa, M.A.: Sobolev–Morrey spaces related to an ultraparabolic equation. Manuscr. Math. 96(3), 371–392 (1998)

Strain, R.M., Guo, Y.: Almost exponential decay near Maxwellian. Commun. Partial Differ. Equ. 31(1–3), 417–429 (2006)

Strain, R.M., Zhu, K.: The Vlasov–Poisson–Landau system in ${\mathbb{R}}_x^3$. Arch. Ration. Mech. Anal. 210(2), 615–671 (2013)

Wu, K.-C.: Global in time estimates for the spatially homogeneous Landau equation with soft potentials. J. Funct. Anal. 266(5), 3134–3155 (2014)

Wu, K.-C.: Pointwise behavior of the linearized Boltzmann equation on a torus. SIAM J. Math. Anal. 46(1), 639–656 (2014)