Results 71 to 80 of about 9,802,344 (402)
Weak-strong uniqueness property for the full Navier-Stokes-Fourier system [PDF]
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]
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
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
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
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
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
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
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]
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
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Conus, Daniel, Khoshnevisan, Davar
openaire +4 more sources