Very weak solutions to the Navier-Stokes system in general unbounded domains

作者：Farwig Reinhard^*; Riechwald Paul Felix

来源：Journal of Evolution Equations, 2015, 15(2): 253-279.

DOI：10.1007/s00028-014-0258-y

• Navier-Stokes equations
• Very weak solutions
• General unbounded domains
• Spaces (L)over-tilde(q)(Omega)

We consider very weak instationary solutions u of the Navier-Stokes system in general unbounded domains , , with smooth boundary, i.e., u solves the Navier-Stokes system in the sense of distributions and where , 2 < r < a. Solutions of this class have no differentiability properties and in general are not weak solutions in the sense of Leray-Hopf. However, they lie in the so-called Serrin class yielding uniqueness. To deal with the unboundedness of the domain, we work in the spaces (instead of ) defined as when but as L (q) + L (2) when 1 < q < 2. The proofs are strongly based on duality arguments and the properties of the spaces .

• 出版日期2015-6