On the Existence of Long-Time Classical Solutions for the 2D Inviscid Boussinesq Equations
On the Existence of Long-Time Classical Solutions for the 2D Inviscid Boussinesq Equations
In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>N</mi> </math> being the buoyancy frequency. It is proved that for general initial data <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <msub> <mrow> <mi>u</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>∈</mo> <msup> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> …