We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1])

In a thin heterogeneous porous layer, we carry out multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density diffusing particles that are subject to coagulation in pairs. Assuming layer is made up microstructures uniformly distributed inside, obtain limit an upscaled model lower space dimension. We also prove corrector-type result very usefu...

which describes stationary reaction-diffusion phenomena but is often also called Helmholtz equation in certain communities. For example in meteorology, the early seminal papers [48, 56] led an entire community to call equations of the form (2) Helmholtz equations, see for example [14]. Even standard texts in applied mathematics now sometimes use the term Helmholtz equation for both (1) and (2),...

In the design of rotary compressor, Helmholtz resonator is always used in the discharge port of cylinder to reduce noise. The effect of Helmholtz resonator on the discharge port is restricted because of the narrow frequency band of Helmholtz resonator. In this paper, multi-Helmholtz resonator on the top-flange is used to reduce the discharge noise of different frequency bands, which does not ch...

In the second volume of the Handbuch der physiologischen Optik, published in 1860, Helmholtz sets out a three-receptor theory of color vision using coterminal response curves, and shows that this theory can unify most phenomena of color mixing known at the time. Maxwell had publicized the same theory five years earlier, but Helmholtz barely acknowledges this fact in the Handbuch. Some historian...