Results 71 to 80 of about 9,802,344 (402)

Weak-strong uniqueness property for the full Navier-Stokes-Fourier system [PDF]

open access: yes, 2011
The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists.
arxiv   +1 more source

Weak solutions to the Navier-Stokes equations [PDF]

open access: yesarXiv, 2022
We prove the equivalence of being a Leray-Hopf weak solution to the Navier-Stokes equations in $\mathbb{R}^m, m \ge 3$, to satisfying a well known integral equation. We use this equation to derive some properties of these weak solutions.
arxiv  

Weak solutions to the Navier-Stokes inequality with arbitrary energy profiles

open access: yes, 2019
In a recent paper, Buckmaster & Vicol (arXiv:1709.10033) used the method of convex integration to construct weak solutions $u$ to the 3D incompressible Navier-Stokes equations such that $\| u(t) \|_{L^2} =e(t)$ for a given non-negative and smooth energy ...
Ożański, Wojciech S.
core   +1 more source

Global Weak Solutions to the Compressible Quantum Navier-Stokes Equations with Damping

open access: yesSIAM Journal on Mathematical Analysis, 2016
In this paper, we proved the existence of global weak solutions of the compressible quantum Navier--Stokes equations with large data in three dimensions (3D).
A. Vasseur, Cheng Yu
semanticscholar   +1 more source

Making tau amyloid models in vitro: a crucial and underestimated challenge

open access: yesFEBS Letters, EarlyView.
This review highlights the challenges of producing in vitro amyloid assemblies of the tau protein. We review how accurately the existing protocols mimic tau deposits found in the brain of patients affected with tauopathies. We discuss the important properties that should be considered when forming amyloids and the benchmarks that should be used to ...
Julien Broc, Clara Piersson, Yann Fichou
wiley   +1 more source

Semi‐supervised classification of fundus images combined with CNN and GCN

open access: yesJournal of Applied Clinical Medical Physics, Volume 23, Issue 12, December 2022., 2022
Abstract Purpose Diabetic retinopathy (DR) is one of the most serious complications of diabetes, which is a kind of fundus lesion with specific changes. Early diagnosis of DR can effectively reduce the visual damage caused by DR. Due to the variety and different morphology of DR lesions, automatic classification of fundus images in mass screening can ...
Sixu Duan   +8 more
wiley   +1 more source

On Indirect Approach to the Solvability of Quasi-Linear Dirichlet Elliptic Boundary Value Problem with BMO-Anisotropic p-Laplacian

open access: yesJournal of Optimization, Differential Equations and Their Applications, 2018
We study here Dirichlet boundary value problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principle part and L^1-control in coefficient of the low-order term.
Peter I. Kogut, Olha P. Kupenko
doaj   +1 more source

The ergodic limit for weak solutions of elliptic equations with Neumann boundary condition

open access: yesMathematics in Engineering, 2021
We consider the so-called {\it ergodic} problem for weak solutions of elliptic equations in divergence form, complemented with Neumann boundary conditions. The simplest example reads as the following boundary value problem in a bounded domain of $\R^N$:
François Murat , Alessio Porretta
doaj   +1 more source

Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system [PDF]

open access: yes, 2011
We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test functions. As a corollary we establish weak-strong uniqueness principle for the compressible Navier-Stokes system.
arxiv   +1 more source

Weak nonmild solutions to some SPDEs

open access: yesIllinois Journal of Mathematics, 2010
17 ...
Conus, Daniel, Khoshnevisan, Davar
openaire   +4 more sources

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