Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations

By Luigi C. Berselli, Giovanni P. Galdi. 2002

190 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e309c66d4e0a79ee23ca8e91ef1b1a02e56bf8db

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure (2007, background): “A number of authors have studied similar conditional regularity results involving either the pressure, or combinations of u and p; see for instance Beir˜ ao da Veiga [2]–[4], Chae–Lee [7], or Berselli–Galdi [ 5 ].”
Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain (2004, background): “Recently the author [25] proved that ifp ∈ L (R3×(0, T ))with 2/α+3/γ ≤ 2 (see also [5]), or ∇p ∈ L (R3 × (0, T )) with 2/α + 3/γ ≤ 3 then the weak solution actually is regular, which is a final result for ∇p in L -type space.”
Remark on a regularity criterion in terms of pressure for the Navier-Stokes equations (2011, result): “Regularity results including assumptions on the pressure have been given by Kaniel [8], and more recently a final result has been obtained by Berselli and Galdi [3] (a much simpler proof was given by Zhou [21], very recently).”
A new regularity criterion for weak solutions to the Navier–Stokes equations (2005, background): “For the regularity criteria in terms of the gradient of velocity or the pressure, we refer to [1, 2, 4, 6, 7, 26, 27, 28].”
On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space (2010, background): “Berselli and Galdi [2] and Chae and Lee [3] obtained regularity criteria for weak solutions in terms of the pressure P or its gradient ∇ P .”
A Strong Regularity Result for Parabolic Equations (2004, background): “The authors proved that u is smooth provided that u0 ∈ W 1,2 and P is bounded from below. See also [ BG ].”
Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor (2010, background): “, [3], [4], [5], [8], [17], [30], [39]).”