Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations

DOI10.1016/S0893-9659(00)00190-7zbMath0982.58024arXivmath/0007027MaRDI QIDQ5938955

Steve Shkoller

Publication date: 7 August 2001

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0007027

zbMATH Keywords

Lagrangian averaged Euler or Euler-\(\alpha\) equationsLagrangian flow maporiented Riemannian 2-manifold

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Applications of PDEs on manifolds (58J90)

Related Items (18)

Grade-two fluids on non-smooth domain driven by multiplicative noise: existence, uniqueness and regularity ⋮ Strong solutions for a stochastic model of two-dimensional second grade fluids driven by Lévy noise ⋮ Instantaneous energy and enstrophy variations in Euler-alpha point vortices via triple collapse ⋮ Weak solutions of a stochastic model for two-dimensional second grade fluids ⋮ Exponential mixing for stochastic model of two-dimensional second grade fluids ⋮ Strong solution for a stochastic model of two-dimensional second grade fluids: existence, uniqueness and asymptotic behavior ⋮ Martingale solution to equations for differential type fluids of grade two driven by random force of Lévy type ⋮ Large deviations for stochastic models of two-dimensional second grade fluids driven by Lévy Noise ⋮ Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence ⋮ Moderate deviations for stochastic models of two-dimensional second grade fluids ⋮ THE VORTEX BLOB METHOD AS A SECOND-GRADE NON-NEWTONIAN FLUID ⋮ Viscosity limit and deviations principles for a grade-two fluid driven by multiplicative noise ⋮ Moderate deviations for stochastic models of two-dimensional second-grade fluids driven by Lévy noise ⋮ Large deviations for stochastic models of two-dimensional second grade fluids ⋮ Vanishing distance phenomena and the geometric approach to SQG ⋮ Random dynamics of two-dimensional stochastic second grade fluids ⋮ Global existence and uniqueness of solutions to the equations of second-grade fluids ⋮ Global well-posedness of second-grade fluid equations in 2D exterior domain

Cites Work

• Existence and uniqueness of classical solutions of the equations of motion for second-grade fluids
• Weak and classical solutions of a family of second grade fluids
• Partial differential equations. 1: Basic theory
• Groups of diffeomorphisms and the motion of an incompressible fluid
• On second grade fluids with vanishing viscosity
• Convergence of Vortex Methods for Euler’s Equations, III
• Unnamed Item

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