[en] Whether or not global solutions of the 2D Navier–Stokes–Cahn–Hilliard (NS–CH) system without full viscosity and mobility can develop finite time singularities is a difficult issue. A major result of this paper deals with global regularity of strong solutions for the NS–CH system with mixed partial viscosity and mobility. In addition, the 2D NS–CH system without viscosity but with full mobility is investigated. In this case, we also prove the global existence and uniqueness of classical solutions. (paper)

[en] We describe the research and development work for the P2 experiment which aims for a high precision determination of the weak mixing angle sin² θ_W to a precision of 0.15% at a four-momentum transfer of 4.5 x 10^-3 GeV². This accuracy, comparable to existing measurements at the Z pole, allows for a sensitive test of the Standard Model up to a mass scale of 50 TeV, extendable to 60 TeV. The weak mixing angle is connected to the weak charge of the proton which will be extracted from a measurement of the parity violating cross section asymmetry -39.94 x 10^-9 in elastic electron-proton scattering. A total accuracy of 0.57 x 10^-9 is achievable in a measurement time of 11000 h using a 150 μA polarized electron beam impinging on a 60 cm liquid hydrogen target. The P2 asymmetry is smaller than any asymmetry measured so far in electron scattering with an unprecedented goal for the accuracy. The use of a solenoid spectrometer with 100% φ-acceptance as well as an atomic hydrogen trap polarimeter are new features, which have never before been used in parity-violation experiments. In order to collect the enormous statistics required for this measurement, the new Mainz Energy-Recovering Superconducting Accelerator (MESA) is under construction. Plans for the associated beam control system and the polarimetry are described in this article as well. A liquid hydrogen high-power target with an extremely low noise level of 10 ppm needs to be designed and constructed. We report in addition on the conceptual design of the P2 spectrometer, its Cherenkov detectors, the integrating read-out electronics as well as the ultra-thin, fast tracking detectors. The physics program of the MESA facility comprises indirect, high precision search for physics beyond the Standard Model, measurement of the neutron distribution in nuclear physics, single-spin asymmetries, and a possible future extension to the measurement of hadronic parity violation. (orig.)