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The paper is concerned with the spatially homogeneous isotropic Boltzmannequation for Bose-Einstein particles with quantum collision kernel where theinteraction potential $\phi({\bf x})$ can be approximately written as the deltafunction plus a certain attractive potential such that the Fourier transform$\widehat{\phi}$ of $\phi$ behaves like $0 \le \widehat{\phi}(\xi) \le {\rmconst.} |\xi|^{\eta}$ for $|\xi|<<1$ for some constant $\eta\ge 1$. We provethat in this case, there is no condensation in finite time for all temperaturesand all solutions, and thus it is completely different from the case$\widehat{\phi}(\xi) \ge {\rm const.}|\xi|^{\eta}$ for $|\xi|<<1$ with $0\le\eta<1/4$ as considered in \cite{Cai-Lu}. For a class of initial data that havesome nice integrability near the origin, we also get some regularity, stabilityand $L^{\infty}$ estimate.

On the spatially homogeneous Boltzmann equation for Bose-Einstein particles with balanced potentials