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\begin{equation}  \begin{aligned}  \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}-K\left(\frac{{\partial }^2u}{\partial x^2}+\frac{{\partial }^2u}{\partial y^2}\right)&=0 \\  \frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+u\frac{\partial x}+v\frac{\partial  v}{\partial y}-K\left(\frac{{\partial }^2v}{\partial x^2}+\frac{{\partial }^2v}{\partial y^2}\right)&=0\ \end{aligned}  \end{equation}