Solutions with Linear Profile of Velocity to the Euler Equations in Several Dimensions

Olga S. Rozanova ()
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Olga S. Rozanova: Moscow State University, Department of Mathematics and Mechanics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 861-870 from Springer

Abstract: Abstract We study the solutions to the Euler equations with the right-hand sides describing diverse external forces: (1) $$ {{\partial }_{{t\rho }}} + div(\rho {\text{V}}) = 0, $$ (2) $$ {{\partial }_{t}}(\rho {\text{V}}) + (\rho {\text{V}},\nabla ){\text{V}} + \nabla p = \rho {\text{f}}({\text{x}},t,{\text{V}},\rho ,S), $$ (3) $$ {{\partial }_{t}}S + ({\text{V}},\nabla S) = 0 $$ with the state equation p = e S ργ, γ =const > 1, the function f is supposed to be smooth with respect to all arguments. Here ρ(t, x), V(t, x), S(t, x) are components of the solution, given in ℝ+ × ℝ n , n ≥ 1 (density, velocity and entropy, correspondingly), p(t, x) is the pressure.

Keywords: Cauchy Problem; Euler Equation; Smooth Solution; Oceanic Physic; Interior Solution (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_81

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DOI: 10.1007/978-3-642-55711-8_81

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