An Introduction to the Navier-Stokes Initial-Boundary Value Problem

By Giovanni P. Galdi. 2000

367 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Fluid Flow and Transfer Processes

View Paper: https://www.semanticscholar.org/paper/e75a0ff74ce58c0eda17cce2889ebcbd91d31573

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In Applied Mathematics

In Computational Mechanics

In Fluid Flow and Transfer Processes

Citations in the corpus

On the energy equality for the 3D Navier–Stokes equations (2018, background): “In addition, if f 2 Ls(⌦), with 1 s 1, then B[f ] 2W 1,s0 (⌦) and moreover it holds (for fixed ) that kfkW 1,s C(s,⌦)kfkLs , see for instance the review in Galdi [27].”
On the Strong Solvability of the Navier—Stokes Equations (2000, methodology): “Hence we can invoke regularity results due to Heywood [40], Sohr [72], and others (see Theorem 5.2 in Galdi’s survey [ 27 ]) to obtain another proof for vq2 C 1 ( _”
Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder (2004, background): “Drag and lift coe cients of a two-dimensional ow around a cylinder are computed very accurately in References [3, 4].”
An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier—Stokes Equations (2000, background): “(See Y. Giga [7], G. P. Galdi [ 6 ].) The question whether the weak solution which nds itself in L 1;3 (QT ) 3 is a strong solution is still open.”
L3,∞-solutions of the Navier-Stokes equations and backward uniqueness (2003, background): “The proof is more or less standard (see, for instance, [9] and [23]) and is based on successive iterations.”
Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces (2019, neutral): “(Sketch) We only sketch the proof, which follows that from Hajduk & Robinson (2017), which in turn is based on the argument presented in Galdi (2000). We approximate u(t) for each t ∈ [0, T ] in such a way that (i) un(t) ∈ Dσ(Ω); (ii) un(t) → u(t) in H 1 0 (Ω) with ‖un(t)‖H1 ≤ C‖u(t)‖H1 ; (iii) un(t”
On the uniqueness of weak solutions of the two-dimensional primitive equations (2003, background): “The reader interested in a review on energy equality and uniqueness questions related to Navier-Stokes is referred to [4] page 22 and the references cited therein.”
REGULARITY OF A SUITABLE WEAK SOLUTION TO THE NAVIER-STOKES EQUATIONS AS A CONSEQUENCE OF REGULARITY OF ONE VELOCITY COMPONENT (2002, background): “in the recent works of H.Kozono [11] and G.P.Galdi [ 4 ].”