scholarly journals A study of the Navier-Stokes equations with the kinematic and Navier boundary conditions

2010 ◽  
Vol 59 (2) ◽  
pp. 721-760 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Zhongmin Qian
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Navier Boundary Conditions

scholarly journals Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Alessio Falocchi ◽  
Filippo Gazzola
Keyword(s):  
Boundary Conditions ◽  
Regular Solution ◽  
Wide Class ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lipschitz Domains ◽  
Navier Stokes Equations ◽  
Navier Boundary Conditions ◽  
Physical Interest ◽  
Uniqueness Of A Solution

<p style='text-indent:20px;'>For the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the uniqueness of a solution is related to the existence of a regular solution. They may be obtained under suitable assumptions on the data and smoothness assumptions on the domain (at least <inline-formula><tex-math id="M1">\begin{document}$ C^{2,1} $\end{document}</tex-math></inline-formula>). With a symmetrization technique, we prove these results in the case of Navier boundary conditions in a wide class of merely <i>Lipschitz domains</i> of physical interest, that we call <i>sectors</i>.</p>

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