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In this paper, we consider the global existence of strong solutions to the incompressible Navier-Stokes equations on the cubic domain in $R^3$. While the global existence for arbitrary data remains as an important open problem, we here provide with some new observations on this matter. We in particular prove the global existence result when ${\Omega}$ is a cubic domain and initial and forcing functions are some linear combination of functions of at most two variables and the like by decomposing the spectral basis differently.
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참고문헌 (16)
참고문헌 신청
R. A. Adams / 1975 / Sobolev Spaces / Academic Press
J. D. Avrin / 1996 / Large-eigenvalue global existence and regularity results for the Navier-Stokes equations / J. Differential Equations 127:365~390
P. Constantin / 1988 / Navier-Stokes equations / University of Chicago Press
Lawrence C. Evans / 1998 / Partial Differential Equations / American Mathematical So-ciety
H. Fujita / 1964 / On the Navier-Stokes initial value problem / Arch. Rational Mech. Anal 16:269~315
J. D. Avrin / 1996 / Large-eigenvalue global existence and regularity results for the Navier-Stokes equations / J. Differential Equations 127:365~390
P. Constantin / 1988 / Navier-Stokes equations / University of Chicago Press
Lawrence C. Evans / 1998 / Partial Differential Equations / American Mathematical So-ciety
H. Fujita / 1964 / On the Navier-Stokes initial value problem / Arch. Rational Mech. Anal 16:269~315
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