an:06657474
Zbl 1358.35093
Khai, D. Q.; Tri, N. M.
Well-posedness for the Navier-Stokes equations with data in homogeneous Sobolev-Lorentz spaces
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 149, 130-145 (2017).
0362-546X
2017
j
35Q30 76D05 76N10
Navier-Stokes equations; mild solutions; existence and uniqueness; homogeneous Sobolev-Lorentz spaces
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 [\textit{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.
Gelu Paşa (Bucureşti)
1049.35517; 0842.35074