The Navier-Stokes equations for linearly growing velocity with nondecaying initial disturbance

Sawada, Okihiro; Usui, Toshiomi

Hokkaido University Preprint Series in Mathematics, 2008, 899, 1-27

Permalink : https://doi.org/10.14943/84253

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アクセス権	open access
DOI	https://doi.org/10.14943/84253
URI	https://hdl.handle.net/2115/69911
タイトル	The Navier-Stokes equations for linearly growing velocity with nondecaying initial disturbance
著者	著者名 Sawada, Okihiro
著者	著者名 Usui, Toshiomi
言語	英語
キーワード	Navier-Stokes equations
	linearly growing initial data
	mild solution
	Besov space
発行日	2008
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	899
ページ	1-27
抄録	The locally-in-time solvability of the Cauchy problem of the incompressible Navier-Stokes equations is established with nitial velocity U0 of the form U0(x) := u0(x) - Mx, where M is a real-valued matrix and u0 is a bounded function. It is also hown that in 2-dimensional case the Navier-Stokes equations admit unique globally-in-time smooth solution, due to the uniform bound for vorticity. Although the semigroup is not analytic, our mild solution satisfies the Navier-Stokes equations in the classical sense, provided the pressure term is suitably chosen. The form of the pressure is uniquely determined, provided the disturbance of velocity is bounded and the modified pressure is in a certain function space.
資源タイプ	紀要論文
出版タイプ	Version of Record