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Well-posedness for the Navier-Stokes equations with data in homogeneous Sobolev-Lorentz spaces. (English) Zbl 1358.35093
This paper is concerning the solutions of Navier-Stokes equations in some specific $$L^{\infty}$$ space when the initial conditions belong to a certain Sobolev-Lorentz space, more general than the cases studied before. A more general result is obtained, compared with [M. Cannone et al., Ondelettes, paraproduits, et Navier-Stokes. Paris: Diderot (1995; Zbl 1049.35517); Methods Appl. Anal. 2, No. 3, 307–319 (1995; Zbl 0842.35074)]. A much weaker condition on the initial data is imposed. The existence of the mild solution is given, when the norm of initial data in a specific Besov space is small enough.

##### MSC:
 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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