Well-posedness for the Navier–Stokes equations with data in homogeneous Sobolev–Lorentz spaces

In this paper, we study local well-posedness for the Navier–Stokes equations (NSE) with arbitrary initial data in homogeneous Sobolev–Lorentz spaces ḢLq,rs(Rd):=(−Δ)−s/2Lq,r for d≥2,q>1,s≥0, 1≤r≤∞, and dq−1≤sd,r=q,s=0 (see Cannone (1995), Cannone and Meyer (1995)), for q=r=2,d2−1...

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Bibliographic Details
Published in:Nonlinear analysis 2017-01, Vol.149, p.130-145
Main Authors: Khai, D.Q., Tri, N.M.
Format: Article
Language:English
Subjects:
Existence and uniqueness of local and global mild solutions
Homogeneous Sobolev–Lorentz spaces
Navier–Stokes equations
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Summary:In this paper, we study local well-posedness for the Navier–Stokes equations (NSE) with arbitrary initial data in homogeneous Sobolev–Lorentz spaces ḢLq,rs(Rd):=(−Δ)−s/2Lq,r for d≥2,q>1,s≥0, 1≤r≤∞, and dq−1≤sd,r=q,s=0 (see Cannone (1995), Cannone and Meyer (1995)), for q=r=2,d2−1
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2016.10.015