scholarly journals Navier-Stokes Equations with Potentials

2007 ◽  
Vol 2007 ◽  
pp. 1-30 ◽  
Author(s):  
Adriana-Ioana Lefter
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Maximal Monotone Operator ◽  
Stokes Equations ◽  
Maximal Monotone ◽  
Existence Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nonlinear Semigroups ◽  
2D And 3D

We study Navier-Stokes equations perturbed with a maximal monotone operator, in a bounded domain, in 2D and 3D. Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. Examples are also provided.

scholarly journals On the construction of suitable weak solutions to the 3D Navier–Stokes equations in a bounded domain by an artificial compressibility method

2017 ◽  
Vol 20 (01) ◽  
pp. 1650064 ◽  
Author(s):  
Luigi C. Berselli ◽  
Stefano Spirito
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation.

scholarly journals Regularity of Weak Solutions to the Inhomogeneous Stationary Navier–Stokes Equations

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1336
Author(s):  
Alfonsina Tartaglione
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Analogous Result ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Hölder Continuous ◽  
Navier Stokes Equations ◽  
Regularity Of Weak Solutions ◽  
Constant Viscosity ◽  
Stationary Navier Stokes Equations

One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equations is the regularity of weak solutions. This problem has been deeply investigated for homogeneous fluids. In this paper, the regularity of the solutions in the case of not constant viscosity is analyzed. Precisely, it is proved that for a bounded domain Ω⊂R2, a weak solution u∈W1,q(Ω) is locally Hölder continuous if q=2, and Hölder continuous around x, if q∈(1,2) and |μ(x)−μ0| is suitably small, with μ0 positive constant; an analogous result holds true for a bounded domain Ω⊂Rn(n>2) and weak solutions in W1,n/2(Ω).

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