Abstract We establish both a local and a global well-posedness theories for the nonlinear Hartree–Fock equations and its reduced analog in the setting of the modulation spaces on In addition, we prove similar results when a harmonic potential is added to the equations. In the process, we prove the boundedeness of certain multilinear operators on products of the modulation spaces which may be of independent interest.

中文翻译：

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调制空间中的 Hartree-Fock 方程

摘要 我们建立了非线性Hartree-Fock方程的局部和全局适定性理论及其在调制空间设置中的简化模拟。此外，我们证明了在方程中加入谐波势时的类似结果。在此过程中，我们证明了某些多线性算子对可能具有独立意义的调制空间乘积的有界性。