## Abstract

We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue spaces. We prove an abstract result referred to fractional power spaces of positive, self-adjoint, compact-inverse operators on Hilbert spaces, and then obtain our main result by using the explicit form of these fractional power spaces for the Dirichlet Laplacian and Stokes operators. As a simple application, we prove that all weak solutions of the convective Brinkman–Forchheimer equations posed on a bounded domain in (Formula presented.) satisfy the energy equality.

Original language | English (US) |
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Pages (from-to) | 759-777 |

Number of pages | 19 |

Journal | Proceedings of the London Mathematical Society |

Volume | 125 |

Issue number | 4 |

DOIs | |

State | Published - Oct 2022 |

## All Science Journal Classification (ASJC) codes

- General Mathematics