Formal improvements in the solution of the wavelet-transformed Poisson and diffusion equations

DOI10.1063/1.532487zbMath0933.35163OpenAlexW2014301377MaRDI QIDQ4701639

Jacques Lewalle

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532487

zbMATH Keywords

wavelet transformPoisson equationHamiltonian formulationNavier-Stokes turbulence

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Turbulence (76F99) General harmonic expansions, frames (42C15)

Related Items (7)

Galerkin analysis for Schrödinger equation by wavelets ⋮ A filtering and wavelet formulation for incompressible turbulence ⋮ Wavelets and orthogonal polynomials based on harmonic oscillator eigenstates ⋮ A class of solutions for the inverse diffusion problem ⋮ Single-scale wavelet representation of turbulence dynamics: formulation and Navier-Stokes regularity ⋮ FIELD RECONSTRUCTION FROM SINGLE SCALE CONTINUOUS WAVELET COEFFICIENTS ⋮ On a wavelet-based method for the numerical simulation of wave propagation

Cites Work

• Wavelet transforms of self-similar processes
• Singularity spectrum of fractal signals from wavelet analysis: Exact results
• Wavelet transforms of some equations of fluid mechanics
• The space and scale dependencies of the self-similar structure of turbulence
• Wavelet spectra compared to Fourier spectra
• BESOV NORMS IN TERMS OF THE CONTINUOUS WAVELET TRANSFORM. APPLICATION TO STRUCTURE FUNCTIONS

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