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We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do- main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of L2 norms of the initial velocity and the gradient of the initial velocity and Lp,2, p ≥ 4 norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.
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참고문헌 (27)
참고문헌 신청
D. Iftimie / 1999 / The 3D Navier-Stokes equations seen as a perturbation of the 2D Navier- Stokes equations / Bull. Soc. Math. France 127 (4) : 473 ~ 517
D. Iftimie / 2001 / Some results on the Navier-Stokes equations in thin 3D domains / J. Differential Equations 169 (2) : 281 ~ 331
D. Iftimie / 2007 / Navier-Stokes equations in thin 3D domains with Navier boundary conditions / Indiana Univ. Math. J 56 (3) : 1083 ~ 1156
E. Hopf / 1951 / Uber die Anfangswertaufgabe fur die hydrodynamischen Grudgleichungen / Math. Nachr 4 : 213 ~ 231
G. R. Sell / 2002 / Dynamics of Evolutionary Equations, In Applied Math. Sciences 143 / Springer
D. Iftimie / 2001 / Some results on the Navier-Stokes equations in thin 3D domains / J. Differential Equations 169 (2) : 281 ~ 331
D. Iftimie / 2007 / Navier-Stokes equations in thin 3D domains with Navier boundary conditions / Indiana Univ. Math. J 56 (3) : 1083 ~ 1156
E. Hopf / 1951 / Uber die Anfangswertaufgabe fur die hydrodynamischen Grudgleichungen / Math. Nachr 4 : 213 ~ 231
G. R. Sell / 2002 / Dynamics of Evolutionary Equations, In Applied Math. Sciences 143 / Springer
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