Global mild solutions of Navier-Stokes equations
Zhen Lei,Fanghua Lin +1 more
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In this article, the authors established a global well-posedness of mild solutions to the Navier-Stokes equations if the initial data are in the space X-1 defined by X -1 = {f E D'(R 3 ): ∫ ℝ 3 |ξ| -1 |f|dξ < ∞}.Citations
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Ill-posedness for the Navier–Stokes equations in critical Besov spaces B˙∞,q−1
TL;DR: In this article, the authors studied the Cauchy problem for the incompressible Navier-Stokes equations in two and higher spatial dimensions and showed that the solution map δ u 0 → u in critical Besov spaces B ˙ ∞, q − 1 ( ∀ q ∈ [ 1, 2 ] ) is discontinuous at origin.
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Long time decay to the Lei–Lin solution of 3D Navier–Stokes equations
TL;DR: In this article, it was shown that if u ∈ C ( [ 0, ∞ ], X − 1 ( R 3 ) ) is a global solution of 3D Navier-Stokes equations, then u ( t ) decays to zero as time goes to infinity.
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Global well-posedness for Navier–Stokes equations in critical Fourier–Herz spaces
Marco Cannone,Gang Wu +1 more
TL;DR: In this paper, the authors prove the global well-posedness of 3D Navier-Stokes equations in critical Fourier-Herz spaces, by making use of the Fourier localization method and the Littlewood-Paley theory.
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Gevrey regularity for a class of dissipative equations with applications to decay
TL;DR: In this article, Gevrey class regularity of solutions to a class of dissipative equations with a general quadratic nonlinearity and a general dissipation including fractional Laplacian is established.
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Global mild solutions of the Landau and non-cutoff Boltzmann equations
TL;DR: In this article, the authors proved the existence of small-amplitude global-in-time unique mild solutions to both the Landau equation including the Coulomb potential and the Boltzmann equation without angular cutoff.
References
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On the Navier-Stokes initial value problem. I
TL;DR: In this article, the authors considered the Navier-Stokes equation for 3-dimensional flows and deduced the existence theorems for 3D flows through a Hilbert space approach, making use of the theory of fractional powers of operators.
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Strong LP-solutions of the Navier-Stokes equation in Rm, with applications to weak solutions
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Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
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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.