P[x_, y_, t_] = [Rho][x, y, t]/([Mu] mu) kb T[x, y, t]  ;
e[x_, y_, t_] = ([Gamma] - 1) [Rho][x, y, t]/([Mu] mu )
kb T[x, y, t];
cp = 5/2 kb/([Mu] mu);
Rgas = 8.3144598;
cv = 5/2 kb/([Mu] mu) - Rgas;
[Gamma] = cp/cv;
g = 28.02*9.81;
[Mu] = 0.6163328197226503`;
mu = 1.66053904*10^-27;
kb = 1.38064852*10^-23;
sol = NDSolve[{D[T[x, y, t], y] ==
 0.41 g [Rho] [x, y, t] T[x, y, t]/P[x, y, t],
D[P[x, y, t], y] == g [Rho][x, y, t],
T[x, 0, t] == 5770, [Rho][x, 0, t] ==
 1.42*10^-7*1.408*10^3}, {[Rho], T}, {y, 0, 4000000}, {x, 0,
12000000}, {t, 0, 10}, StartingStepSize -> 200000,
Method -> "ExplicitEuler"];
sol1 = NDSolve[{
D[[Rho][x, y, t]*u[x, y, t],
 t] == -D[[Rho][x, y, t]*u[x, y, t]*u[x, y, t] + P[x, y, t], x] -
  D[[Rho][x, y, t]*u[x, y, t]*v[x, y, t], y],
 D[[Rho][x, y, t]*v[x, y, t],
 t] == -D[[Rho][x, y, t]*v[x, y, t]*u[x, y, t], x] -
 D[[Rho][x, y, t]*v[x, y, t]*v[x, y, t] + P[x, y, t], y] +
 g [Rho][x, y, t],
 D[[Rho][x, y, t], t] == -D[[Rho][x, y, t]*u[x, y, t], x] -
 D[[Rho][x, y, t]*v[x, y, t], y],
 D[e[x, y, t], t] == -D[u[x, y, t]*e[x, y, t], x] -
 D[v[x, y, t]*e[x, y, t], y] -
 P[x, y, t]*(D[u[x, y, t], x] - D[v[x, y, t], y]),
 v[0, y, t] == v[12000000, y, t],
 u[0, y, t] == u[12000000, y, t],
 T[0, y, t] == T[12000000, y, t],
[Rho][0, y, t] == [Rho][12000000, y, t],
P[0, y, t] == P[12000000, y, t],
e[0, y, t] == e[12000000, y, t],
P[x, 0, t] == (P[x, 0, 0] /. sol),
e[x, 0, t] == (e[x, 0, 0] /. sol),
v[x, 4000000, t] == 0,
v[x, 0, t] == 0,
v[x, y, 0] == 0,
u[x, y, 0] == 0,
T[x, y, 0] == (T[x, y, 0] /. sol),
[Rho][x, y, 0] == ([Rho][x, y, 0] /. sol)
},
{u, v, T, [Rho]}, {x, 0, 12000000}, {y, 0, 4000000}, {t, 0, 10},
StartingStepSize -> 200000, Method -> "ExplicitEuler"]

DynamicNDSolve`FiniteDifferenceDerivativeFunction::ddim: Data {{{5770.},        {8554.72},{11339.4},{14124.1},{16908.9},{19693.6},{22478.3},{25263.},{28047.7},{30832.4},{33617.2},{36401.9},{39186.6}},<<23>>,{{5770.},{8554.72},{11339.4},{14124.1},{16908.9},{19693.6},{22478.3},{25263.},{28047.7},{30832.4},{33617.2},{36401.9},{39186.6}}} is not a rectangular tensor with dimensions {24,13}.