WebJun 25, 2008 · R. Danchin, M. Paicu This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension First we prove a global existence result for data in Lorentz spaces satisfying a smallness condition which is at the scaling of the equations. WebThe Mathematics 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; Introductory statistics; and Geometric transformations and congruence. Khan Academy's Mathematics 1 course is built to …
Raphaël Danchin: Recent approaches based on harmonic
WebMay 17, 2024 · The incompressible navier-stokes equations in vacuum Raphaël Danchin, Piotr Boguslaw Mucha We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonnegative density. WebMar 31, 2024 · R. Danchin, Global existence in critical spaces for compressible Navier-Stokes equations, Invent. Math., 141 (2000), 579-614. doi: 10.1007/s002220000078. [9] R. Danchin, Local theory in critical spaces for compressible viscous and heat-conductive gases, Comm. Partial Differential Equations, 26 (2001 reach 2010 programs
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WebMar 29, 2024 · This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author (s). Managing Editor Jean-Benoît Bost, Wilhelm Schlag … WebPreviously Danchin and Paicu [16] studied the global well-posedness of (1.2) with the Yudovich-type data for the case when ν = 0 and β = 2. In addition, Hmidi and Zerguine [25] studied the global regularity of (1.2) with ν = 0 and β ∈ (1,2], but with an initial data (u 0,θ 0) in a more regular functional setting. As our first step, we ... how to split rrif income