Displaying similar documents to “Uniqueness of weak solutions of the Navier-Stokes equations”

Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ n

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

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For a bounded domain Ω ⊂ ℝ n , n ≥ 3 , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system - Δ u + u · ∇ u + ∇ p = f , div u = k , u | ∂ Ω = g with u ∈ L q , q ≥ n , and very general data classes for f , k , g such that u 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...

Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods

Basil Nicolaenko, Alex Mahalov, Timofey Shilkin (2006-2007)

Séminaire Équations aux dérivées partielles

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We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space L 3 ( R 3 ) . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally L 3 . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.

Steady compressible Navier-Stokes-Fourier system in two space dimensions

Petra Pecharová, Milan Pokorný (2010)

Commentationes Mathematicae Universitatis Carolinae

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We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation p ( ρ , θ ) ∼ ρ γ + ρ θ , where ρ is the density and θ is the temperature. For γ > 2 , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness...