Kozono, Hideo Global \(L^ n\)-solution and its decay property for the Navier-Stokes equations in half-space \(R^ n_ +\). (English) Zbl 0715.35062 J. Differ. Equations 79, No. 1, 79-88 (1989). The existence and uniqueness of a global strong \(L^ n\)-solution as well as an \(L^ n\)-decay result are shown for the Navier-Stokes equations in \({\mathbb{R}}^ n_+\times (0,\infty)\) for small initial data. Compared to similar results the proof is complete and simplified. A main tool consists in the implicit function theorem which allows to conclude the \(L^ n\)-continuity of the solution with respect to the initial data. Reviewer: H.Jeggle Cited in 39 Documents MSC: 35Q30 Navier-Stokes equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:existence; uniqueness; global strong \(L^ n\)-solution; decay result; implicit function theorem PDFBibTeX XMLCite \textit{H. Kozono}, J. Differ. Equations 79, No. 1, 79--88 (1989; Zbl 0715.35062) Full Text: DOI References: [1] Borchers, W.; Miyakawa, T., \(L^2\)-decay for the Navier-Stokes flow in half space, Math. Ann., 282, 139-155 (1988) · Zbl 0627.35076 [2] Borchers, W.; Sohr, H., On the semigroup of the Stokes operator for exterior domains in \(L^q\)-spaces, Math. Z., 196, 415-425 (1987) · Zbl 0636.76027 [3] Giga, Y.; Miyakawa, T., Solution in \(L_r\) of the Navier-Stokes initial value problem, Arch. Rational Mech. Anal., 89, 267-281 (1985) · Zbl 0587.35078 [4] Kato, T., Strong \(L^p\)-solution of the Navier-Stokes equations in \(\textbf{R}^m \), with applications to weak solutions, Math. Z., 187, 471-480 (1984) · Zbl 0545.35073 [5] Masuda, K., Lecture at Waseda University (1984) [6] Tanabe, H., Equation of Evolution (1979), Pitman: Pitman London [7] Ukai, S., A solution formula for the Stokes equation in \(\textbf{R}_+^n \), Comm. Pure Appl. Math., 40, 611-621 (1987) · Zbl 0638.76040 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.