Cannone, Marco; Planchon, Fabrice On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations. (English) Zbl 0965.35121 Rev. Mat. Iberoam. 16, No. 1, 1-16 (2000). The authors consider the Cauchy problem for the Navier-Stokes equations by reducing to the integral equation \[ u(x,t)=S(t) u_{0}(x)-\int_{0}^{t}\mathbf{P} S(t-s) \nabla \cdot (u \otimes u) (x,s) ds,\tag{1} \] where \(S(t)=\exp (t \Delta)\) is the heat kernel, \(\mathbf{P}\) is a pseudo-differential operator. Let \(u(x,t)\) be a solution of (1) in \(L^3 (\mathbb{R})\) on \(x\) and in \(C[0,T)\) on \(t\) with initial data \(u_0 \in L^3\), \(w:=u-S(t) u_0\), then \(w \in H \times C[0,T)\). Here \(H\) is a Sobolev space. Reviewer: Vladimir Mityushev (Paris) Cited in 19 Documents MSC: 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids Keywords:Navier-Stokes equations; Besov space PDFBibTeX XMLCite \textit{M. Cannone} and \textit{F. Planchon}, Rev. Mat. Iberoam. 16, No. 1, 1--16 (2000; Zbl 0965.35121) Full Text: DOI EuDML