On the Strong Solvability of the Navier—Stokes Equations

By Herbert Amann. 2000

267 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/af32cad391c69f85af74fa1319e4a3cb36cab090

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Maximal Lp – Lq-Estimates for the Stokes Equation: a Short Proof of Solonnikov’s Theorem (2010, result): “For recent results on layers, general unbounded domains and other boundary conditions we refer to the work of Amann [ Ama00 ], Shibata and Shimizu ([SS03]), Abels [Abe05], Farwig, Kozono and Sohr [FKS05] and Bothe and Pr¨uss ([BP06]).”
Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations (2005, background): “The historical details describing the achievement of this result are contained in [37] and for a systematic approach of the existence and uniqueness problem for mild solutions, the reader is also referred to the papers of Amann [1].”
Stationary Stokes, Oseen and Navier–Stokes Equations with Singular Data (2011, result): “Amann, H.: On the strong solvability of the Navier-Stokes equations.”
On the uniqueness of time-periodic solutions to the Navier–Stokes equations in unbounded domains (2009, methodology): “This fact was shown by Amann [1] for the case f ∈ C([0, T ]; Dn), while the case f = 0 was demonstrated by Lions-Masmoudi [26].”
A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces (2009, methodology): “Apq, which indicates either B s pq or F s pq, is applied to various partial differential equations (see, for example, [1–2]).”
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, methodology): “Versions of the multiplier theorems on the real line can be found in [2], [20], [21] (this reference contains criteria implying the R−boundedness property for operator families), [33] and [34].”
A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in W−1/q,q (2005, background): “More recently, Amann has investigated exi stence, uniqueness and regularity of very weak solutions for the initialboundaryvalue problem for the Navier-Stokes equations, under very general conditions on the boundary data [3], [4]; see also Grubb [19].”
On optimal initial value conditions for local strong solutions of the Navier–Stokes equations (2009, background): “Since then there have been developed several sufficient initial value conditions for the existence of local strong solutions, getting weaker step by step and enlarging the corresponding solution class, see [9,12,14,16,18,20,21,23], and the recent results in [2].”
The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations (2002, background): “Amann [1] gave a systematic and comprehensive research for the Navier-Stokes equation upon the Besov spaces (see also Kobayashi-Muramatsu [24] for an abstract setting case).”
NAVIER-STOKES EQUATIONS IN THE BESOV SPACE NEAR L∞ AND BMO (2003, background): “great effort has been made to prove the existence of the strong solution in spaces larger than L such as the Morrey space Mr , the Lorentz space Lr,∞ and the Besov space B p,q (Giga et al [15], Giga and Miyakawa [14], Kozono and Yamazaki [19, 20], Sohr [24], Cannone [5], Cannone and Meyer [6], Amann”