An analysis of typical microphysical systems is presented in the hydrodynamic formulation of quantum mechanics. The emphasis is on the physical peculiarities appearing in the hydrodynamic picture, and on the mathematical treatment of the nonlinear quantum-hydrodynamic Geld equations. Further, quantum-hydrodynamic uncertainty relations are derived, which relate the minimum uncertainty products to the interior quantum stresses.

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Based on the Galilean relativity principle and Maxwell's equations, electromagnetic field equations are derived for inertial frames, in which the substratum of the electromagnetic waves flows with arbitrary velocity | w | < c (velocity of light). It is demonstrated that the electromagnetic field equations with electromagnetic substratum flow are strictly covariant against Galilei transformations. Wave equations, conservation and invariance theorems, and boundary conditions are derived for the electrodynamic fields in presence of electromagnetic substratum flow. Initial‐boundary‐value problems are solved for electromagnetic signal propagation and induction in the substratum by an integral equation method. Physical effects for the measurement of the velocity field of the electromagnetic substratum are discussed. Maxwell's conception that his equations refer to a frame of reference with resting electromagnetic substratum is confirmed, and it is shown that Maxwell's equations are also applicable to inertial frames with small substratum velocities, | w | ≪ c.

Es wird das nichtlineare Randwertproblem formuliert, das die räumliche Entwicklung der Grenzschicht in einer leitenden Flüssigkeit beschreibt, die bei Vorhandensein eines äußeren Druckgradienten quer zu einem inhomogenen Magnetfeld entlang einer ebenen Platte strömt. Mit Hilfe von Transformationen, Reihenentwicklungen und Integrationsverfahren (Sattelpunkt‐Methode), wie sie von Meksyn in die Analysis hydrodynamischer Grenzschichten eingeführt worden sind, werden analytische Lösungen für das Geschwindigkeitsfeld sowohl in Punkten der anliegenden als auch der abgelösten magnetohydrodynamischen Strömung gewonnen. Der Anwendung auf magnetohydrodynamische Diffusor‐Strömungen wird besondere Aufmerksamkeit geschenkt. Es wird gezeigt, daß ein inhomogenes Magnetfeld die Grenzschichtablösung unterdrücken kann.

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