Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation

Regularity Criteria for the 2d Boussinesq Equations with Supercritical Dissipation∗

This paper focuses on the 2D incompressible Boussinesq equations with fractional dissipation, given by Λαu in the velocity equation and by Λβθ in the temperature equation, where Λ= √−Δ denotes the Zygmund operator. Due to the vortex stretching and the lack of sufficient dissipation, the global regularity problem for the supercritical regime α+β<1 remains an outstanding problem. This paper prese...

The 2d Boussinesq-navier-stokes Equations with Logarithmically Supercritical Dissipation

This paper studies the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator L that can be defined through both an integral kernel and a Fourier multiplier. When the symbol of L is represented by |ξ| a(|ξ|) with a satisfying lim|ξ|→∞ a(|ξ|) |ξ|σ = 0 for any σ > 0, we obtain the global well-posedness. A special cons...

The 2D Incompressible Boussinesq Equations

The Two-Dimensional Incompressible Boussinesq Equations with General Critical Dissipation

The two-dimensional incompressible Boussinesq equations with partial or fractional dissipation have recently attracted considerable attention and the global regularity issue has been extensively investigated. This paper aims at the global regularity in the case when the dissipation is critical. The critical dissipation refers to α + β = 1 when Λα ≡ (−Δ)α2 and Λβ represent the fractional Laplaci...

Exponential Decay of Energy for Some Nonlinear Hyperbolic Equations with Strong Dissipation

Yaojun Ye Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou 310023, China Correspondence should be addressed to Yaojun Ye, [email protected] Received 14 December 2009; Revised 21 May 2010; Accepted 4 August 2010 Academic Editor: Tocka Diagana Copyright q 2010 Yaojun Ye. This is an open access article distributed under the Creative...