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Gravitational Hartree equation

{c}

The gravitational Hartree flow conserves
$$
M(u)=\int|u|^2,
\qquad
E(u)=\frac12\int|\nabla u|^2-\frac14\int|\nabla\phi|^2.
$$
The self-adjointness of the Newtonian convolution turns the time derivative of the potential energy into $\operatorname{Re}\int\phi u\overline{u_t}$, which cancels the derivative of the kinetic energy by the equation.

= Hartree mass conservation
{synonym}

= Hartree energy conservation
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Hartree mass and energy conservation

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codex/hartree-energy-conservation

Hartree mass and energy conservation

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Hartree mass and energy conservation

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