Stability to the Incompressible Navier-Stokes Equations by Guilong Gui
By Guilong Gui
This thesis includes result of Dr. Guilong Gui in the course of his PhD interval with the purpose to appreciate incompressible Navier-Stokes equations. it's dedicated to the learn of the steadiness to the incompressible Navier-Stokes equations. there's nice capability for additional theoretical and numerical study during this box. The concepts constructed in conducting this paintings are anticipated to be important for different actual version equations. it's also hopeful that the thesis may well function a precious reference on present advancements in study issues on the topic of the incompressible Navier-Stokes equations. It was once nominated through the Graduate college of chinese language Academy of Sciences as an exceptional PhD thesis.
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Additional resources for Stability to the Incompressible Navier-Stokes Equations
Example text
Pisa (2004) 16. : On the Navier-Stokes initial value problem I. Arch. Rat. Mech. Anal. 16, 269–315 (1964) 17. : Strong L p -solutions of the Navier-Stokes equations in Rm with applications to weak solutions. Math. Z. 187, 471–480 (1984) 18. : Solutions autosimilaires des équations de Navier-Stokes, Séminaire Équations aux Dérivées Partielles de l’École Polytechnique, 1993–1994 19. : Théorémes d’unicité pour le systéme de Navier-Stokes tridimensionnel. J. Anal. Math. 77, 27–50 (1999) 20. : Well-posedness for the Navier-Stokes equations.
Ii) Let s ∈ R, 1 ≤ p, r ≤ ∞. Then u belongs to B sp,r if and only if there exists {c j,r } j∈N such that c j,r r = 1 and ˙ ju Lp ≤ Cc j,r 2− js u B˙ sp,r . In order to obtain a better description of the regularizing effect of the transportdiffusion equation, we will use Chemin-Lerner type spaces L λT ( B˙ sp,r (R3 )) from [19, 39]. 3 Let s ≤ 3p (resp. s ∈ R), (r, λ, p) ∈ [1, +∞]3 and T ∈]0, +∞]. We define L λT ( B˙ sp r (R3 )) as the completion of C([0, T ], S(R3 )) by the norm f L λT ( B˙ sp,r ) def = T 2qr s q∈Z 0 ˙ q f (t) λ Lp dt r λ 1 r < ∞.
9, 187–195 (1962) 22 1 Introduction 6. : Un teorema di unicità per le equazioni di Navier-Stokes. Ann. Mat. Pure. Appl. 48, 173–182 (1959) 7. : Interior regularity of weak solutions of the time-dependent Navier-Stokes equation. Proc. Japan Acad. 36, 273–277 (1960) 8. : Solutions for semilinear Parabolic equations in L p and regularity of weak solutions of the Navier-Stokes system. J. Differ. Equ. 62, 186–212 (1986) 9. : On L 3, ∞ -solutions to the Navier-Stokes equations and backward uniqueness.