Local existence of ℓ∞ solutions of the euler equations of incompressible perfect fluids

1976 ◽  
pp. 184-194 ◽  
Author(s):  
R. Temam
Keyword(s):  
Euler Equations ◽  
Local Existence ◽  
Perfect Fluids

Local existence with low regularity for the 2D compressible Euler equations

2021 ◽  
Vol 18 (03) ◽  
pp. 701-728
Author(s):  
Huali Zhang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Euler Equations ◽  
Local Existence ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Spatial Derivative ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Local Solutions

We prove the local existence, uniqueness and stability of local solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial data of velocity, density, specific vorticity [Formula: see text] and the spatial derivative of specific vorticity [Formula: see text].

The Theory of Special Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Euler Equations ◽  
Lorentz Transformation ◽  
Electromagnetic Force ◽  
Momentum Tensor ◽  
Perfect Fluids ◽  
Dimensional Spacetime ◽  
Tensor Formulation ◽  
Basic Equations

This chapter shows how the principle of special relativity and the principle of the constancy of the velocity of light uniquely determine the Lorentz transformation. Unlike in pre-relativity physics, space and time are not separate entities. They are combined into a four-dimensional spacetime continuum, which is most clearly demonstrated in the formulation of the theory of special relativity due to Hermann Minkowski. The chapter then defines vectors and tensors with respect to the Lorentz transformation, leading to a tensor formulation of Maxwell's equations, of the electromagnetic force acting on charges and currents, and of the energy-momentum of the electromagnetic field and its conservation law. It also introduces the energy-momentum tensor of matter and discusses the basic equations of the hydrodynamics of perfect fluids (the Euler equations).

Local existence for the stochastic Euler equations with Lévy noise

2019 ◽  
Vol 113 (1-2) ◽  
pp. 1-27
Author(s):  
Igor Kukavica ◽  
Fanhui Xu
Keyword(s):  
Euler Equations ◽  
Local Existence ◽  
Lévy Noise ◽  
Levy Noise
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