Boltzmann Equation with a Large Potential in a Periodic Box

The stability of the Maxwellian of the Boltzmann equation with a large amplitude external potential Φ has been an important open problem. In this paper, we resolve this problem with a large C−potential in a periodic box T, d ≥ 3. We use [1] in Lp−L∞ framework to establish the well-posedness and the L∞−stability of the Maxwellian μE(x, v) = exp { − |v| 2 2 − Φ(x) } .