Global regularity for the 2D Boussinesq equations with partial viscosity terms

By Dongho Chae. 2006

541 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8c618c736ab8794f3e298aa63de798e28fd4a4f

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 Mathematical Physics

Citations in the corpus

Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion (2009, unknown): “In this case, we obtain the following global a priori bound for ω = ∇ × u and j = ∇ × b, ∥∥ω(t)∥∥22 + ∥∥j (t)∥∥22 + η t∫ 0 ∥∥∇j (τ )∥∥22 dτ C(η)(∥∥ω(0)∥∥22 + ∥∥j (0)∥∥22) for t 0, where C(η) is a constant depending on η only.”
Nonlinear maximum principles for dissipative linear nonlocal operators and applications (2011, background): “The well-posedness of (B0,2) and (B2,0) have been obtained in [5, 19], while the scaling critical cases (B1,0) and (B0,1) have been resolved in [20] and [21] respectively.”
Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data (2008, result): “In addition, those smooth data belong to all the Sobolev spaces Hs. Hence, applying Chae’s result [ 6 ] provides us with a sequence of smooth global solutions (θn, un)n∈N which belong to all the spaces C(R+; Hs).”
Global regularity for the 2D anisotropic Boussinesq Equations with vertical dissipation (2011, methodology): “[9] D. Chae and H.-S. Nam, Local existence and blow-up criterion for the Boussinesq equations, Proc.”
Global Well-Posedness of the 2D Boussinesq Equations with Vertical Dissipation (2015, background): “The initial data in [3, 14] are required to have some suitable high regularities.”
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, 6, 10, 15], for example.”
On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity (2007, methodology): “We smooth out the initial data and so we obtain from the result of [ 4 ] the existence of a family of unique global solutions (vn, n). It follows from the a priori estimates that this family is bounded in our solving”
Continuous data assimilation for the 2D Bénard convection through velocity measurements alone (2014, unknown): “For recent results concerning the two-dimensional Boussinesq equations we refer the reader to [7], [11], [21], [23], [24], [29], and references therein.”
GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO (2008, background): “Under various regularity assumptions on the initial data, it has been shown that for arbitrarily large initial data, systems (B�,0) with κ > 0 and (B0,�) with ν > 0 admit a global unique solution (see for example [1, 7 , 13, 14, 15, 19, 20]).”