Strong solutions of the Boussinesq system in exterior domains
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Christian Komo
Abstract
We consider the instationary Boussinesq equations in a smooth three-dimensional exterior domain. A strong solution is a weak solution such that the velocity field additionally satisfies Serrin's condition. The crucial point in this concept of a strong solution is the fact that we have required no additional integrability condition for the temperature. We present a sufficient criterion for the existence of such a strong solution. Further we will characterize the class of initial values that allow the existence of such a strong solution in a sufficiently small interval. Finally, we will obtain a uniqueness criterion for weak solutions of the Boussinesq equations which is based on the identification of a weak solution with a strong solution.
The author thanks Reinhard Farwig for his kind support.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
- Strong solutions of the Boussinesq system in exterior domains
- Some stability results on global solutions to the Navier–Stokes equations
- The Navier–Stokes–Fourier system: From weak solutions to numerical analysis
- Global regularity for a model Navier–Stokes equations on ℝ3
- The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain
Artikel in diesem Heft
- Frontmatter
- Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
- Strong solutions of the Boussinesq system in exterior domains
- Some stability results on global solutions to the Navier–Stokes equations
- The Navier–Stokes–Fourier system: From weak solutions to numerical analysis
- Global regularity for a model Navier–Stokes equations on ℝ3
- The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain
