The Energy Balance Relation for Weak solutions of the Density-Dependent Navier-Stokes Equations
Trevor M. Leslie,Roman Shvydkoy +1 more
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In this article, the authors considered the incompressible inhomogeneous Navier-Stokes equations with constant viscosity coefficient and density, and showed that the energy balance relation holds for weak solutions if the velocity, density and pressure belong to a range of Besov spaces of smoothness 1/3.About:
This article is published in Journal of Differential Equations.The article was published on 2016-09-15 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Navier–Stokes equations & Bounded function.read more
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Regularity and Energy Conservation for the Compressible Euler Equations
TL;DR: In this paper, the authors give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved.
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Regularity and Energy Conservation for the Compressible Euler Equations
TL;DR: In this paper, the authors give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved.
Journal ArticleDOI
Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit
TL;DR: In this paper, the authors relax this assumption, requiring only interior Holder regularity and continuity of the normal component of the energy flux near the boundary, which is consistent with the possible formation of a Prandtl-type boundary layer in the vanishing viscosity limit.
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Energy Conservation for the Weak Solutions of the Compressible Navier–Stokes Equations
TL;DR: In this paper, the energy conservation for weak solutions of the compressible Navier-Stokes equations was shown for any time t ≥ 0, under certain conditions, and the results hold for the renormalized solutions with constant viscosities, as well as the weak solutions with degenerate viscosity.
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Statistical solutions and Onsager’s conjecture
TL;DR: In this article, a version of Onsager's conjecture on conservation of energy for the incompressible Euler equations in the context of statistical solutions was shown to hold for weak solutions under a weaker Besov-type regularity assumption.
References
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Book
Turbulence: The Legacy of A. N. Kolmogorov
TL;DR: In this article, the authors present a modern account of turbulence, one of the greatest challenges in physics, put into historical perspective five centuries after the first studies of Leonardo and half a century after the attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers.
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Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models
TL;DR: In this article, the Navier-Stokes equations and the Euler equations are studied in the context of nonlinear partial differential equations (NPDE) and their applications in applied mathematics.
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Onsager's conjecture on the energy conservation for solutions of Euler's equation
TL;DR: In this article, a simple proof of a result conjectured by Onsager on energy conservation for weak solutions of Euler's equation is given for weak Euler solvers.
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The Euler equations as a differential inclusion
TL;DR: In this article, a new point of view on weak solutions of the Euler equations is proposed, describing the motion of an ideal incompressible fluid in R n with n 2.