标题： Oberbeck-Boussinesq系统的具有牛顿引力场的大自相似解 显示英文标题

标题： Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field

摘要： 考虑整个三维空间中不可压缩流体的纳维-斯托克斯方程与传热方程的耦合系统。 该系统在适当的缩放下是不变的。 使用Leray-Schauder定理和紧致性论证，我们构造了该系统的自相似解，而无需对齐次初始条件施加任何小性假设。 显示英文摘要

摘要： The Navier-Stokes system for an incompressible fluid coupled with the equation for a heat transfer is considered in the whole three dimensional space. This system is invariant under a suitable scaling. Using the Leray-Schauder theorem and compactness arguments, we construct self-similar solutions to this system without any smallness assumptions imposed on homogeneous initial conditions.