Junction Conditions, Resolution of Singularities and Nonlinear Equations of Physics
Elemer E Rosinger
TL;DR
This paper establishes necessary and sufficient conditions for solutions with discontinuities across hyper-surfaces in polynomial nonlinear PDEs, including Navier-Stokes, General Relativity, and Magneto-Hydrodynamics.
Contribution
It provides a unified framework for analyzing discontinuous solutions in complex nonlinear PDE systems relevant to physics.
Findings
Conditions for existence of discontinuous solutions derived
Applicable to Navier-Stokes, General Relativity, Magneto-Hydrodynamics
Advances understanding of singularities in nonlinear PDEs
Abstract
For large classes of systems of polynomial nonlinear PDEs necessary and sufficient conditions are given for the existence of solutions which are discontinuous across hyper-surfaces. These PDEs contain the Navier-Stokes equations, as well as those of General Relativity and Magneto-Hydrodynamics.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Mathematical Analysis and Transform Methods · Algebraic and Geometric Analysis