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pro vyhledávání: '"Iyer, Sameer"'
We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $\omega^{(NS)} = 1 + \epsilon \omega$, set on the channel $\mathbb{T} \times [-1, 1]$, supplemented with Navier boundary conditions on the perturbation, $\omega|_{y = \
Externí odkaz:
http://arxiv.org/abs/2405.19249
In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to Couette in $\mathbb T \times [-1,1]$ with vanishing diffusivity $\nu \t
Externí odkaz:
http://arxiv.org/abs/2405.19233
Autor:
Iyer, Sameer, Maekawa, Yasunori
The Triple-Deck equations are a classical boundary layer model which describes the asymptotics of a viscous flow near the separation point, and the Couette flow is an exact stationary solution to the Triple-Deck equations. In this paper we prove the
Externí odkaz:
http://arxiv.org/abs/2405.10532
Autor:
Iyer, Sameer
The (favorable) Falkner-Skan boundary layer profiles are a one parameter ($\beta \in [0,2]$) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle $\beta \frac{\pi}{2}$. The most famous mem
Externí odkaz:
http://arxiv.org/abs/2403.07791
In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $\mathbb{T} \times [-1,1]$, supplemented with Navier boundary conditions $\omega|_{y = \pm 1} = 0$. Initial datum is taken to be a perturbati
Externí odkaz:
http://arxiv.org/abs/2311.00141
We study the boundary layer theory for slightly viscous stationary flows forced by an imposed slip velocity at the boundary. According to the theory of Prandtl (1904) and Batchelor (1956), any Euler solution arising in this limit and consisting of a
Externí odkaz:
http://arxiv.org/abs/2308.15447
We give a proof of linear inviscid damping and vorticity depletion for non-monotonic shear flows with one critical point in a bounded periodic channel. In particular, we obtain quantitative depletion rates for the vorticity function without any symme
Externí odkaz:
http://arxiv.org/abs/2301.00288
Autor:
Iyer, Sameer, Masmoudi, Nader
In this paper, we study the higher regularity theory of a mixed-type parabolic problem. We extend the recent work of \cite{DMR} to construct solutions that have an arbitrary number of derivatives in Sobolev spaces. To achieve this, we introduce a cou
Externí odkaz:
http://arxiv.org/abs/2212.08735
We establish linearized well-posedness of the Triple-Deck system in Gevrey-$\frac32$ regularity in the tangential variable, under concavity assumptions on the background flow. Due to the recent result \cite{DietertGV}, one cannot expect a generic imp
Externí odkaz:
http://arxiv.org/abs/2205.15829
Autor:
Iyer, Sameer, Masmoudi, Nader
We demonstrate the existence of an open set of data which exhibits \textit{reversal} and \textit{recirculation} for the stationary Prandtl equations (data is taken in an appropriately defined product space due to the simultaneous forward and backward
Externí odkaz:
http://arxiv.org/abs/2203.02845