The Helmholtz decomposition in arbitrary unbounded domains - a theory beyond
On a Decay Property of Weak Solution for Semilinear Evolution Equation of Parabolic Type and Its Applications.
Two-dimensional Navier-Stokes flow in unbounded domains.
Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.
Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
On a new class of generalized solutions for the Stokes equations in exterior domains
Asypmtotic Behaviour in Lr for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin's condition
Let u be a weak solution of the Navier-Stokes equations in a smooth bounded domain Ω ⊆ ℝ³ and a time interval [0,T), 0 < T ≤ ∞, with initial value u₀, external force f = div F, and viscosity ν > 0. As is well known, global regularity of u for general u₀ and f is an unsolved problem unless we pose additional assumptions on u₀ or on the solution u itself such as Serrin’s condition where 2/s + 3/q = 1. In the present paper we prove several local and global regularity properties by using assumptions...
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