Journal ArticleDOI
Strong LP-solutions of the Navier-Stokes equation in Rm, with applications to weak solutions
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Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
Journal ArticleDOI
The Cauchy problem for the critical nonlinear Schro¨dinger equation in H s
Thierry Cazenave,F. B. Weissler +1 more
Journal ArticleDOI
Well-posedness for the Navier–Stokes Equations
Herbert Koch,Daniel Tataru +1 more
TL;DR: In this paper, the NavierStokes equations are locally well-posed for smooth enough initial data as long as one imposes appropriate boundary conditions on the pressure at ∞, where u is the velocity and p is the pressure.
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Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system
TL;DR: In this paper, a local regular solution for the Navier-Stokes system was constructed for a class of semilinear parabolic equations with dimensionless or scaling invariant norm, where p and q are chosen so that the norm of Lq(0, T; Lp) is dimensionless.
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L3,∞-solutions of the Navier-Stokes equations and backward uniqueness
TL;DR: In this article, it was shown that the L3,∞-solutions of the Cauchy problem for the 3D Navier-Stokes equations are smooth.
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Journal Article
Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'Hydrodynamique.
Journal Article
On the nonstationary Navier-Stokes system
Tosio Kato,Hiroshi Fujita +1 more
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.math.unipd.org/conditions) of the agreement with the Rendiconti del Seminario Matematico della Università di Padova are discussed.