# NAVIER-STOKES EQUATIONS IN THE BESOV SPACE NEAR $L^\infty$ AND $BMO$ NAVIER-STOKES EQUATIONS IN THE BESOV SPACE NEAR L∞ AND BMO

## Abstract

We prove a local existence theorem for the Navier-Stokes equations with the initial data in $B_{\infin,\infin}^{0}$ containing functions which do not decay at infinity. Then we establish an extension criterion on our local solutions in terms of the vorticity in the homogeneous Besov space $\middot{B}_{\infin,\infin}^{0}$.

We prove a local existence theorem for the Navier-Stokes equations with the initial data in <i>B</i><sup>0</sup><sub>∞,∞</sub> containing functions which do not decay at infinity. Then we establish an extension criterion on our local solutions in terms of the vorticity in the homogeneous Besov space <i>B</i><sup>·0</sup><sub>∞,∞</sub>.

## Journal

• Kyushu Journal of Mathematics

Kyushu Journal of Mathematics 57(2), 303-324, 2003

Kyushu University

## Codes

• NII Article ID (NAID)
110001263203
• NII NACSIS-CAT ID (NCID)
AA10994346
• Text Lang
ENG
• Article Type
Departmental Bulletin Paper
• ISSN
1340-6116
• Data Source
NII-ELS  IR  J-STAGE

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