I’m trying to numerically solve the following equation

$$frac{partial{u}}{partial{t}}=Dnabla^2u-vec{v}.nabla(u)$$

for which -1 $le$ x $le$ 1, -1 $le$ y $le$ 1, 0 $le$ t $le$ 1 with initial condition u(0,x,y)=sin(πxy) and u(t,x,y)=sin(πxy) and D=0.1 and $vec{v}$ is {y,-x}.

I’ve tried doing the following

```
eqn2 = Inactive(0.1*Laplacian(u(t, x, y), {t, x, y}) - {y, -x}*Gradient(u(t,x,y),{t, x, y}))
pdesol = DSolve({eqn2, u(0, x, y) == Sin((Pi) x y), u(t, x, y) == Sin(Pi x y)}, u(t, x, y), {x, -1, 1}, {y, -1, 1}, {t, 0, 1})
```

But an error occurs. I have also tried to use NDSolve, but I get the same error, which is, “equation or list of equations expected instead of…”. How could I fix this?