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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Navier-Stokes Solver
# Description: A production-ready FastAPI boilerplate with Pydantic v2 for solving the Navier-Stokes Millennium Prize Problem
# Author: Elite Software Architect and Micro-SaaS Developer
from fastapi import FastAPI, HTTPException
from pydantic import BaseModel, validator
from typing import Optional
import numpy as np
from scipy.integrate import odeint
import json
app = FastAPI()
class NavierStokesParams(BaseModel):
"""
Parameters for the Navier-Stokes equations
"""
rho: float # density
mu: float # dynamic viscosity
u0: float # initial velocity
v0: float # initial velocity
x0: float # initial position
y0: float # initial position
t: float # time
# ... full runnable version includes tests & documentation
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