Dissipation mechanics and exact solutions for nonlinear equations of dissipative type. Principle and application of dissipation mechanics. I
Basing on the complementarity principle we build up a dissipation mechanics theory. It is a dissipative theory of correspondence with quantum mechanics. From this theory we can jointly handle problems of macroscopic non-equilibrium thermodynamics and viscous hydrodynamics, and handle each dissipative and irreversible problem in quantum mechanics. We prove the basic equations of dissipation mechanics to eigenvalues equations of correspondence with the Schrödinger equation or Dirac equation. We merge the basic nonlinear equations of dissipative type, especially the Navier-Stokes equation as a basic equation for macroscopic non- equilibrium thermodynamics and viscous hydrodynamics into integrability condition of basic equation of dissipation mechanics. We obtain exact solutions by the inverse scattering method.
macroscopic non-equilibrium thermodynamics
scientific article; zbMATH DE number 4018585
scientific article