The two-species Vlasov–Maxwell–Landau system in 3
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 5, pp. 1099-1123.

We consider the global classical solutions near the Maxwellians to the two-species Vlasov–Maxwell–Landau system in the whole space. It is shown that the cancelation properties between two species coupled with the electric effect yield the faster time decay of the electric field, which leads to our construction of global solutions.

DOI: 10.1016/j.anihpc.2014.05.005
Classification: 82C40,  82D05,  82D10,  35B40
Keywords: Vlasov–Maxwell–Landau system, Global solution, Time decay, Energy method
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     author = {Wang, Yanjin},
     title = {The two-species {Vlasov{\textendash}Maxwell{\textendash}Landau} system in $ {\mathbb{R}}^{3}$
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     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1099--1123},
     publisher = {Elsevier},
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Wang, Yanjin. The two-species Vlasov–Maxwell–Landau system in $ {\mathbb{R}}^{3}$
      . Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 5, pp. 1099-1123. doi : 10.1016/j.anihpc.2014.05.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.05.005/

[1] P. Degond, M. Lemou, Dispersion relations for the linearized Fokker–Planck equation, Arch. Ration. Mech. Anal. 138 no. 2 (1997), 137 -167 | MR | Zbl

[2] R.J. Duan, Global smooth dynamics of a fully ionized plasma with long-range collisions, Ann. Inst. Henri Poincaré, Anal. Non Linéaire (2013), http://dx.doi.org/10.1016/j.anihpc.2013.07.004 | Numdam | MR

[3] R.J. Duan, R.M. Strain, Optimal large-time behavior of the Vlasov–Maxwell–Boltzmann system in the whole space, Commun. Pure Appl. Math. 24 no. 11 (2011), 1497 -1546 | MR | Zbl

[4] R.J. Duan, T. Yang, H.J. Zhao, Global solutions to the Vlasov–Poisson–Landau system, arXiv:1112.3261v1

[5] R.J. Duan, T. Yang, H.J. Zhao, The Vlasov–Poisson–Boltzmann system in the whole space: the hard potential case, J. Differ. Equ. 252 no. 12 (2012), 6356 -6386 | MR | Zbl

[6] R.J. Duan, T. Yang, H.J. Zhao, The Vlasov–Poisson–Boltzmann system for soft potentials, Math. Models Methods Appl. Sci. 23 no. 6 (2013), 979 -1028 | MR | Zbl

[7] R.J. Duan, S.Q. Liu, T. Yang, H.J. Zhao, Stability of the nonrelativistic Vlasov–Maxwell–Boltzmann system for angular non-cutoff potentials, Kinet. Relat. Models 6 no. 1 (2013), 159 -204 | MR | Zbl

[8] L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Inc., Prentice Hall (2004) | MR | Zbl

[9] Y. Guo, The Landau equation in a periodic box, Commun. Math. Phys. 231 no. 3 (2002), 391 -434 | MR | Zbl

[10] Y. Guo, The Vlasov–Maxwell–Boltzmann system near Maxwellians, Invent. Math. 153 no. 3 (2003), 593 -630 | MR | Zbl

[11] Y. Guo, The Vlasov–Poisson–Landau system in a periodic box, J. Am. Math. Soc. 25 no. 3 (2012), 759 -812 | MR | Zbl

[12] F. Hilton, Collisional transport in plasma, Handbook of Plasma Physics, vol. I: Basic Plasma Physics, North-Holland, Amsterdam (1983)

[13] T. Hosono, S. Kawashima, Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system, Math. Models Methods Appl. Sci. 16 no. 11 (2006), 1839 -1859 | MR | Zbl

[14] N. Ju, Existence and uniqueness of the solution to the dissipative 2D Quasi-Geostrophic equations in the Sobolev space, Commun. Math. Phys. 251 no. 2 (2004), 365 -376 | MR | Zbl

[15] R.M. Strain, The Vlasov–Maxwell–Boltzmann system in the whole space, Commun. Math. Phys. 268 no. 2 (2006), 543 -567 | MR | Zbl

[16] R.M. Strain, Y. Guo, Stability of the relativistic Maxwellian in a collisional plasma, Commun. Math. Phys. 251 no. 2 (2004), 263 -320 | MR | Zbl

[17] R.M. Strain, Y. Guo, Almost exponential decay near Maxwellian, Commun. Partial Differ. Equ. 31 no. 1–3 (2006), 417 -429 | MR | Zbl

[18] R.M. Strain, Y. Guo, Exponential decay for soft potentials near Maxwellian, Arch. Ration. Mech. Anal. 187 no. 2 (2008), 287 -339 | MR | Zbl

[19] R.M. Strain, K. Zhu, The Vlasov–Poisson–Landau system in x 3 , Arch. Ration. Mech. Anal. 210 no. 2 (2013), 615 -671 | MR | Zbl

[20] Y.J. Wang, Golobal solution and time decay of the Vlasov–Poisson–Landau system in 3 , SIAM J. Math. Anal. 44 no. 5 (2012), 3281 -3323 | MR | Zbl

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