Global well-posedness of the 3-dimensional Navier-Stokes initial value problem in $L^p\cap L^2$ with $3<p<\infty$

Abstract

By using the continuous induction method, we prove that the initial value problem of the three dimensional Navier-Stokes equations is globally well-posed in $L^p({\mathbb{R}}^3)\cap L^2({\mathbb{R}}^3)$ for any $3<p<\infty$. The proof is rather simple.

This paper has been withdrawn by the author due to a crucial error in the proof of the main result

References in corpus (2)

• An alternative approach to regularity for the Navier-Stokes equations in critical spaces
• Weak Solutions for the Navier-Stokes Equations for $B_{\infty \infty }^{-1(ln)}+B_{{\dot{X}}_r}^{-1+r,\frac{2}{1-r}}+L^2$ Initial Data

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