KdV on an incoming tide

Given smooth step-like initial data V(0, x) on the real line, we show that the Korteweg–de Vries equation is globally well-posed for initial data u ( 0 , x ) ∈ V ( 0 , x ) + H − 1 ( R ) . The proof uses our general well-posedness result (2021 arXiv:2104.11346). As a prerequisite, we show that KdV is globally well-posed for H 3 ( R ) perturbations of step-like initial data. In the case V ≡ 0, we obtain a new proof of the Bona–Smith theorem (Bona and Smith 1975 Trans. R. Soc. A 278 555–601) using the low-regularity methods that established the sharp well-posedness of KdV in H −1 (Killip and Vişan 2019 Ann. Math. 190 249–305).

How the distribution of colonies of the hydroid Laomedea flexuosa is limited to a narrow belt along the lower littoral zone

In the White Sea the colonial hydroid Laomedea flexuosa inhabits a narrow belt of the lower littoral zone. How is so limited a habitat determined? We studied the time of planula release and the behaviour of larvae during the free-swimming stage and settlement in natural and laboratory conditions. Three methods were used to record the tidal-dependent dynamic of planula release: (1) plankton collecting bags around Fucus distichus macrophytes with mature hydroid colonies; (2) active stirring of Fucus with hydroids in a container with water, which is an old way to stimulate planula release; and (3) direct counts of the mature planulae in gonangia. The dynamic intensity of L. flexuosa planula release was investigated according to 3–4 phases of the tidal cycle. A moment of general release of larvae was shown to be correlated with a period of low water. Following the incoming tide keeps planulae in the littoral area. The planulae of L. flexuosa have a short period of swimming (less than 30 minutes), unlike those of Gonothyrae loveni and Dynamena pumila whose swimming period is about 36 hours. Quick settlement and tidal planula release could explain the strong spatial limitation in the distribution of L. flexuosa within the lower level of the intertidal zone. It is hypothesized that distribution over large areas is most likely by drift of colonies attached to detached seaweeds. Our outlook about the biological ways of ecological niche differentiation among marine organisms is broadened by the results of this study.

Trophic relationships between itinerant fish and crab larvae in a temperate Australian saltmarsh

Comparisons of zooplankton inputs and outputs for a temperate Australian saltmarsh demonstrate a substantial contribution of crab larvae to the ebbing tide water, particularly during the cooler months. Few crab larvae were present in the incoming tide (mean abundance 4 m−3), whereas many crab larvae were present in the outgoing water (mean abundance 2124.63 m−3). Stomach content analysis of itinerant fish exiting the saltmarsh with the ebbing tide demonstrated extremely high proportions of crab larvae in the gut of glassfish (Ambassis jacksoniensis), as well as flat tail mullet (Liza argentea) and blue eye (Pseudomugil signifer). The results suggest a direct trophic link between secondary production of saltmarsh and itinerant fish, and a significant ecological role for burrowing crabs occupying saltmarshes in temperate Australia in the trophic food web of saltmarsh–estuarine systems.