Partial Regularity of Stationary Navier-Stokes Systems under Natural Growth Condition

2019 ◽  
Vol 39 (1) ◽  
pp. 94-110 ◽  
Author(s):  
Lianhua He ◽  
Zhong Tan
Keyword(s):  
Growth Condition ◽  
Partial Regularity ◽  
Navier Stokes ◽  
Natural Growth ◽  
Natural Growth Condition ◽  
Stokes Systems

scholarly journals Regularity Result for Quasilinear Elliptic Systems with Super Quadratic Natural Growth Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Shuhong Chen ◽  
Zhong Tan
Keyword(s):  
Growth Condition ◽  
Elliptic Systems ◽  
Regularity Result ◽  
Boundary Regularity ◽  
Quadratic Growth ◽  
Natural Growth ◽  
General Criterion ◽  
Natural Growth Condition ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under natural growth condition with super quadratic growth and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on interior partial regularity, this result yields an upper bound on the Hausdorff dimension of the singular set at the boundary.

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