Global existence for 3D Navier-Stokes equations in a long periodic domain
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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.
Abstract
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.
참고문헌 (16)
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