论文标题
具有物理应用的非扩展活动标量方程的疾病/适应性
Ill/well-posedness of non-diffusive active scalar equations with physical applications
论文作者
论文摘要
我们考虑使用经营者$ \ mathbf {t} $获得的构成法律的一般类别的活动标量方程，该法律是[0,2] $中的订单$ r_0 \的单数。对于$ r_0 \ in（0,1] $，我们在gevrey spaces $ g^s $中均具有$ s \ in [1，\ frac {1} {r_0}）$的范围，而对于$ r_0 \ in [1,2] $ in [1,2] $，以及在$ \ \ mathbf {t} $上的进一步条件，我们是$ prove nill-pore g s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $然后，我们将疾病/适合性的结果应用于几个特定的非扩展活性标量方程，包括磁性型型方程，不可压缩的多孔培养基方程和奇异的不可压缩的多孔介质方程。
We consider a general class of non-diffusive active scalar equations with constitutive laws obtained via an operator $\mathbf{T}$ that is singular of order $r_0\in[0,2]$. For $r_0\in(0,1]$ we prove well-posedness in Gevrey spaces $G^s$ with $s\in[1,\frac{1}{r_0})$, while for $r_0\in[1,2]$ and further conditions on $\mathbf{T}$ we prove ill-posedness in $G^s$ for suitable $s$. We then apply the ill/well-posedness results to several specific non-diffusive active scalar equations including the magnetogeostrophic equation, the incompressible porous media equation and the singular incompressible porous media equation.
