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[کتاب][B] The mathematical analysis of the incompressible Euler and Navier-Stokes equations: an introduction
J Bedrossian, V Vicol - 2022 - books.google.com
The aim of this book is to provide beginning graduate students who completed the first two
semesters of graduate-level analysis and PDE courses with a first exposure to the …
semesters of graduate-level analysis and PDE courses with a first exposure to the …
Global-in- Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows
In this work, we establish the convergence of 2D, stationary Navier-Stokes flows,
$(u^\epsilon, v^\epsilon) $ to the classical Prandtl boundary layer, $(\bar {u} _p,\bar {v} _p) …
$(u^\epsilon, v^\epsilon) $ to the classical Prandtl boundary layer, $(\bar {u} _p,\bar {v} _p) …
Justification of Prandtl ansatz for MHD boundary layer
The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics
system with Prandtl boundary layer expansion when no-slip boundary condition is imposed …
system with Prandtl boundary layer expansion when no-slip boundary condition is imposed …
Separation for the stationary Prandtl equation
In this paper, we prove that separation occurs for the stationary Prandtl equation, in the case
of adverse pressure gradient, for a large class of boundary data at x= 0 x=0. We justify the …
of adverse pressure gradient, for a large class of boundary data at x= 0 x=0. We justify the …
The inviscid limit and boundary layers for Navier-Stokes flows
The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes
equations modeling viscous incompressible flows converge to solutions of the Euler …
equations modeling viscous incompressible flows converge to solutions of the Euler …
[HTML][HTML] A well-posedness theory for the Prandtl equations in three space variables
The well-posedness of the three space dimensional Prandtl equations is studied under
some constraint on its flow structure. Together with the instability result given in [28], it gives …
some constraint on its flow structure. Together with the instability result given in [28], it gives …
Well-posedness of the hydrostatic Navier–Stokes equations
We address the local well-posedness of the hydrostatic Navier–Stokes equations. These
equations, sometimes called reduced Navier–Stokes/Prandtl, appear as a formal limit of the …
equations, sometimes called reduced Navier–Stokes/Prandtl, appear as a formal limit of the …
Global well-posedness and regularity of weak solutions to the Prandtl's system
Z **n, L Zhang, J Zhao - SIAM Journal on Mathematical Analysis, 2024 - SIAM
We continue our study on the global solution to the two-dimensional Prandtl's system for
unsteady boundary layers in the class considered by Oleinik, provided that the pressure is …
unsteady boundary layers in the class considered by Oleinik, provided that the pressure is …
Regularity and expansion for steady Prandtl equations
Due to degeneracy near the boundary, the question of high regularity for solutions to the
steady Prandtl equations has been a longstanding open question since the celebrated work …
steady Prandtl equations has been a longstanding open question since the celebrated work …
Boundary layer separation and local behavior for the steady Prandtl equation
W Shen, Y Wang, Z Zhang - Advances in Mathematics, 2021 - Elsevier
In this paper, we prove the boundary layer separation of the steady Prandtl equation for
Oleinik's data ensuring the local existence of the solution under suitable adverse pressure …
Oleinik's data ensuring the local existence of the solution under suitable adverse pressure …