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We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in H1 and the forcing function in Lp([0; T);L2),T > 0, 2 p +1 satisfy a certain condition. This condition commonly appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain ϵ tends to zero.
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참고문헌 (16)
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 / Applied Math. Sciences 143
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 / Applied Math. Sciences 143
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