scholarly journals Global well-posedness of the Cauchy problem for the Navier-Stokes equations of nonisentropic flow with discontinuous initial data

1992 ◽  
Vol 95 (1) ◽  
pp. 33-74 ◽  
Author(s):  
David Hoff
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Discontinuous Initial Data ◽  
The Cauchy Problem

scholarly journals Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

2017 ◽  
Vol 3 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Azzeddine El Baraka ◽  
Mohamed Toumlilin
Keyword(s):  
Cauchy Problem ◽  
Stokes Equations ◽  
Morrey Spaces ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Small Initial Data ◽  
Localization Method ◽  
Fourier Localization ◽  
The Cauchy Problem

Abstract In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].

scholarly journals Properties at potential blow-up times for Navier-Stokes

2017 ◽  
Vol 35 (2) ◽  
pp. 127 ◽  
Author(s):  
Paulo R. Zingano ◽  
Jens Lorenz
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Incompressible Flows ◽  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Solution Properties ◽  
Maximal Interval ◽  
Navier Stokes Equations ◽  
The Cauchy Problem

In this paper we consider the Cauchy problem for the 3D navier-Stokes equations for incompressible flows. The initial data are assume d to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solution can develop singularities in finite time. Assuming the maximal interval of existence to be finite, we give a unified discussion of various known solution properties as time approaches the blow-up time.

scholarly journals Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Qinghua Zhang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Parabolic Equations ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Interpolation Spaces ◽  
Navier Stokes Equations ◽  
Sectorial Operators ◽  
The Cauchy Problem

We study the Cauchy problem of the quasilinear evolution equations in Lμp-spaces. Based on the theories of maximal Lp-regularity of sectorial operators, interpolation spaces, and time-weighted Lp-spaces, we establish the local posedness for a class of abstract quasilinear evolution equations with lower regular initial data. To illustrate our results, we also deal with the second-order parabolic equations and the Navier-Stokes equations in Lp,q-spaces with temporal weights.

Sign in / Sign up

Export Citation Format

Share Document