Sharp Strichartz estimates for water waves systems

Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical Strichartz estimates for gravity-capillary waves; for both 2D and 3D waves. Here, by optimal we mean the gains of regularity (over the Sobolev embedding from Sobolev spaces to H\"older spaces) obtained for the linearized systems. Our proofs combine the paradifferential reductions of Alazard-Burq-Zuily with a dispersive estimate using a localized wave package type parametrix of Koch-Tataru.Comment: Some typos fixe

SOME ISSUES OF DEVELOPMENT OF JAPAN 'S FISHERIES SECTOR AND LESSONS LEARNED FROM THE DEVELOPMENT OF VIETNAM 'S FISHERIES SECTOR IN THE CURRENT CONTEXT

With the development of the marine economy in the current context, Vietnam desperately needs models of marine economic development of countries with strengths in the field of marine economic development, especially sustainable development based on the values of aquatic resources brought by marine areas. Japan has much potential for marine economic development because the country has a long coastline and rich marine resources. The article focuses on the study of fisheries development issues for Japan, based on which some experiences are synthesized to create a basis for proposing solutions to develop Vietnam's fisheries sector in a sustainable trend to improve the effectiveness and efficiency of Vietnam's marine economic policy in the current context. Keywords: Fisheries Sector, Aquaculture, Seafood, Sustainable Development