### Abstract

We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large-time behavior of the solution is also obtained.

Original language | English |
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Pages (from-to) | 2261-2300 |

Number of pages | 40 |

Journal | Communications in Mathematical Sciences |

Volume | 16 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Communications in Mathematical Sciences*, vol. 16, no. 8, pp. 2261-2300. https://doi.org/10.4310/CMS.2018.v16.n8.a9

**Smoothing effects and decay estimate of the solution of the linearized two species Landau equation.** / Lin, Yu Chu; Wang, Haitao; Wu, Kung Chien.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Smoothing effects and decay estimate of the solution of the linearized two species Landau equation

AU - Lin, Yu Chu

AU - Wang, Haitao

AU - Wu, Kung Chien

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large-time behavior of the solution is also obtained.

AB - We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large-time behavior of the solution is also obtained.

UR - http://www.scopus.com/inward/record.url?scp=85066497193&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066497193&partnerID=8YFLogxK

U2 - 10.4310/CMS.2018.v16.n8.a9

DO - 10.4310/CMS.2018.v16.n8.a9

M3 - Article

AN - SCOPUS:85066497193

VL - 16

SP - 2261

EP - 2300

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

SN - 1539-6746

IS - 8

ER -