论文标题
Hartree-fock-Bogoliubov方程的全球估计
Global estimates for the Hartree-Fock-Bogoliubov equations
论文作者
论文摘要
我们证明，某些Sobolev型规范比节能的规范稍强，及时保持统一和$ n $。这允许人们在全球及时扩展第二和第三作者的局部存在结果。证明基于摩拉维型型估计值的相互作用和Strichartz估计（包括一些新的终点结果），用于方程$ \ {\ frac {\ frac {1} {i} {i} \partial_t-Δ_{x} x}-Δ__{y} {y}坐标，例如$ l^p（dt）l^q（dx）l^2（dy）$，$ l^p（dt）l^q（dy）l^2（dx）$，$ l^p（dt）l^q（d（x-y）l^2（x-y））l^2（d（x+y））$。主要的新技术成分是混合坐标中的分散估计，这本身可能引起人们的关注。
We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and $N$. This allows one to extend the local existence results of the second and third author globally in time. The proof is based on interaction Morawetz-type estimates and Strichartz estimates (including some new end-point results) for the equation $\{ \frac{1}{i}\partial_t-Δ_{x}-Δ_{y}+\frac{1}{N}V_N(x-y) \}Λ(t, x, y) =F$ in mixed coordinates such as $L^p(dt) L^q(dx) L^2(dy)$, $L^p(dt) L^q(dy) L^2(dx)$, $L^p(dt) L^q(d(x-y)) L^2(d(x+y))$. The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.
