The Helmholtz decomposition in arbitrary unbounded domains - a theory beyond
Störungskriterien im reflexiven Banachraum.
Optimale lokale Existenzsätze für die Gleichungen von Navier-Stokes.
Über die Existenz von Wellenoperatoren für zeitabhängige Störungen.
Ein neues Surjektivitätskriterium im Hilbertraum.
Störungstheoretische Regularitätsuntersuchungen.
Über die Selbstadjungiertheit von Schrödinger Operatoren.
Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes.
Erweiterung eines Satzes von Serrin über die Gleichungen von Navier-Stokes.
A new perturbation criterion for two nonlinear m-accretive operators with applications to semilinear equations.
On Energy Inequality, Smoothness and Large Time Behavior in L2 for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
On Operators with Bounded Imaginary Powers in Banach Spaces.
On the Semigroup of the Stokes Operator for Exterior Domains in Lq-Spaces.
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
Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in
For a bounded domain , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system , , with , , and very general data classes for , , such that may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...
On the Singular Set and the Uniqueness of Weak Solutions of the Navier-Stokes Equations.
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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