Remarks on the Well-Posedness of the Euler Equations in the Triebel–Lizorkin Spaces
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DOI: 10.1007/s00041-021-09837-y
Abstract: We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [ 6 , 7 , 9 ]. The proof… read more here.
Keywords: triebel lizorkin; posedness euler; remarks well; lizorkin spaces ... See more keywords
On the Local Type I Conditions for the 3D Euler Equations
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DOI: 10.1007/s00205-018-1254-0
Abstract: AbstractWe prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution $${v\in L^\infty (-1,0; L^2 ( B(x_0,r)))\cap L^\infty_{{\rm loc}} (-1,0; W^{1, \infty} (B(x_0,… read more here.
Keywords: type conditions; equations local; euler equations; local type ... See more keywords
Global Existence of Near-Affine Solutions to the Compressible Euler Equations
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DOI: 10.1007/s00205-019-01387-4
Abstract: We establish the global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into a vacuum. Vacuum states can occur with either smooth or singular… read more here.
Keywords: global existence; compressible euler; existence; solutions compressible ... See more keywords
An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and $$L_2$$L2 stability
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DOI: 10.1007/s00211-019-01027-9
Abstract: The objective of this article is to characterize the entropy and $$L_2$$L2 stability of several representative discontinuous Galerkin (DG) methods for solving the compressible Euler equations. Towards this end, three DG methods are constructed: one… read more here.
Keywords: compressible euler; semi discrete; euler equations; entropy stability ... See more keywords
$$\rho $$ρ-White noise solution to 2D stochastic Euler equations
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DOI: 10.1007/s00440-019-00902-8
Abstract: A stochastic version of 2D Euler equations with transport type noise in the vorticity is considered, in the framework of Albeverio–Cruzeiro theory (Commun Math Phys 129:431–444, 1990) where the equation is considered with random initial… read more here.
Keywords: euler; euler equations; rho white; equation ... See more keywords
A Grid-Insensitive LDA Method on Triangular Grids Solving the System of Euler Equations
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DOI: 10.1007/s10915-016-0323-5
Abstract: The performance of the classic upwind-type residual distribution (RD) methods on skewed triangular grids are rigorously investigated in this paper. Based on an improved signals distribution, an improved second order RD method based on the… read more here.
Keywords: system euler; method; lda method; euler equations ... See more keywords
Mean Field Limit of Interacting Filaments for 3D Euler Equations
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DOI: 10.1007/s10955-018-2189-4
Abstract: The 3D Euler equations, precisely local smooth solutions of class $$H^s$$Hs with $$s>5/2$$s>5/2 are obtained as a mean field limit of finite families of interacting curves, the so called vortex filaments, described by means of… read more here.
Keywords: euler equations; mean field; limit interacting; field limit ... See more keywords
A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations
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DOI: 10.1007/s11425-018-9529-8
Abstract: For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied when the distance between the holes dε is equal to… read more here.
Keywords: permeability; geometry; regularity holes; euler equations ... See more keywords
On the theory of Besov–Herz spaces and Euler equations
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DOI: 10.1007/s11856-017-1519-6
Abstract: In this paper we consider Euler equations (E) for an incompressible ideal fluid filling the whole space ℝn for n ≥ 2. We prove local-in-time wellposedness and give a blow-up criterion for (E) in a… read more here.
Keywords: herz spaces; spaces euler; besov herz; theory besov ... See more keywords
The incompressible Euler equations under octahedral symmetry: Singularity formation in a fundamental domain
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DOI: 10.1016/j.aim.2021.108091
Abstract: We consider the 3D incompressible Euler equations in vorticity form in the following fundamental domain for the octahedral symmetry group: $\{ (x_1,x_2,x_3): 0 read more here.
Keywords: singularity formation; euler equations; incompressible euler;
Physics-informed neural networks for high-speed flows
Sign Up to like & getrecommendations! Published in 2020 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2019.112789
Abstract: Abstract In this work we investigate the possibility of using physics-informed neural networks (PINNs) to approximate the Euler equations that model high-speed aerodynamic flows. In particular, we solve both the forward and inverse problems in… read more here.
Keywords: high speed; euler equations; problem; physics ... See more keywords