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This paper deals with a study on the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a flat torus. The main objective is to show that the global-in-time weak solution of the Oberbeck-Boussinesq system has global regularity with some condition only on the speed field, i.e., without imposing any restrictions on the temperature.

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On the Regularity of the Oberbeck-Boussinesq Equations

  • 会议论文

  • 发表日期：

    2026年

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  • Haroldo R. Clark,
  • Eduardo Notte-Cuello,
  • Marko Rojas-Medar

摘要

This paper deals with a study on the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a flat torus. The main objective is to show that the global-in-time weak solution of the Oberbeck-Boussinesq system has global regularity with some condition only on the speed field, i.e., without imposing any restrictions on the temperature.