WebDefinition of smallness 1 as in diminutiveness the quality or state of being little in size my grandmother was surprised by the smallness of the latest electronic devices Synonyms & … WebJan 24, 2024 · Moreover, we also obtain the existence of the strong solution for small initial data, the smallness conditions of which are given by the suitable Sobolev norms. In this paper, we address the Hall-MHD equations with partial dissipation. Applying some important inequalities (such as the logarithmic Sobolev inequality using BMO space, bilinear ...
(PDF) Asymptotic Integration of Linear Differential Equations Subject …
WebNov 2, 2024 · In the presence of the fluid filed, the results, by comparison, fall short of the previous ones in the absence of the fluid part. We prove two results: the existence of unique strong solutions locally in time and a blow-up criterion, and the existence of unique strong solutions globally in time with some smallness condition on initial data. WebJan 25, 2024 · Moreover, we also prove that there exists a global unique solution in H N (R 3) for any N ≥ 2, without any other smallness condition of the initial data. ACKNOWLEDGMENTS. This work was supported by the National Natural Science Foundation of China under Grant Nos. 11731014, 11571254, and 11571118 and by the … the pc must secure boot
[2111.01344] On the existence and temporal asymptotics of …
WebNov 14, 2024 · A Smallness Condition Ensuring Boundedness in a Two-dimensional Chemotaxis-Navier—Stokes System involving Dirichlet Boundary Conditions for the Signal … WebMay 9, 2011 · We prove existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension , valid under a smallness condition … WebThe present paper is devoted to study the well-posedness issue of solutions of the 3-D Boussinesq system with damping in the whole space. By means of Littlewood-Paley analysis tools we relax the smallness condition and deal with the nonlinear coupling between the horizontal components and the vertical one with the temperature. Finally, we prove that … the pcod - thyroid book