Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data

By Raphaël Danchin, Marius Paicu. 2008

200 citations recorded by the source corpus.

The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption on the initial temperature, there exists a global unique solution. No smallness conditions are imposed on the data. The global existence issues for infinite energy initial velocity, and for the Bénard system are also discussed.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/045101ad3f338b5474f05795de8a6e25e1f1edb7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

On a maximum principle and its application to logarithmically critical Boussinesq system (2009, background): “The global existence of Yudovich solutions for this system was treated in [10].”
GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO (2008, background): “ξ|ξ 1| σfb(ξ)dξ. Remark 2. Further in the paper, we shall also state the global existence of ﬁnite energy weak solutions corresponding to less regular initial data (see Theorem 10). Remark 3. Like in [15], in all the statements pertaining to System (2), one may replace the assumption thatR u0 ∈ L2 (”
Global Regularity for Some Oldroyd‐B Type Models (2013, background): “A lot of works have been devoted recently to the two-dimensional Boussinesq system with partial dissipation [3], [10], [12], [6] for example.”
Global Well-Posedness for Euler–Boussinesq System with Critical Dissipation (2010, background): “More recently, the study of global existence of Yudovich solutions for this system has been done in [14].”
Global regularity for the 2D anisotropic Boussinesq Equations with vertical dissipation (2011, unknown): “Other interesting recent results on the 2D Boussinesq equations can be found in [1, 2, 3, 11, 12, 15, 16, 24].”
Global regularity results for the 2D Boussinesq equations with vertical dissipation (2011, unknown): “Other interesting recent results on the 2D Boussinesq equations can be found in [1,9,10,12,13, 17,20,22].”