On the regularity of the heat equation solution in non-cylindrical domains: Two approaches

2011 ◽  
Vol 218 (5) ◽  
pp. 1623-1633 ◽  
Author(s):  
Arezki Kheloufi ◽  
Boubaker-Khaled Sadallah
Keyword(s):  
Heat Equation ◽  
Equation Solution ◽  
Cylindrical Domains

scholarly journals The Heat Equation Solution Near the Interface Between Two Media

2017 ◽  
Vol 24 (3) ◽  
pp. 339-352 ◽  
Author(s):  
Natalia T. Levashova ◽  
Olga A. Nikolaeva
Keyword(s):  
Heat Equation ◽  
Equation Solution

Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary

2008 ◽  
Vol 15 (3) ◽  
pp. 517-530
Author(s):  
Makram Hamouda ◽  
Roger Temam
Keyword(s):  
Singular Perturbation ◽  
Heat Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Navier Stokes Equations ◽  
Equation Solution ◽  
Characteristic Boundary ◽  
Thin Region ◽  
Perturbation Problems

Abstract We prove the existence of a strong corrector for the linearized incompressible Navier–Stokes solution on a domain with characteristic boundary. This case is different from the noncharacteristic case considered in [Hamouda and Temam, Some singular perturbation problems related to the Navier–Stokes equations: Springer Verlag, 2006] and somehow physically more relevant. More precisely, we show that the linearized Navier–Stokes solutions behave like the Euler solutions except in a thin region, close to the boundary, where a certain heat equation solution is added (the corrector). Here, the Navier–Stokes equations are considered in an infinite channel of but our results still hold for more general bounded domains.

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