An exact, time-dependent analytical solution for the magnetic field in the inner heliosheath

Abstract We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both induction equation of ideal magnetohydrodynamics in limit infinite electric conductivity and divergence constraint. To this end, we assume that is frozen into a plasma flow resembling characteristic interaction solar wind with local interstellar medium. Furthermore, make use Ohm’s law vector potential scalar potential. By employing suitable gauge condition relates potentials working coordinate representation, thus obtain inhomogeneous first-order system ordinary differential equations Then, using general system, compute via curl relation. Finally, analyze well-posedness corresponding Dirichlet-type initial-boundary value problem, specify compatibility conditions values, outline implementation conditions.