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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 @validator('rho', 'mu', 'u0', 'v0', 'x0', 'y0', 't') def validate_params(cls, v): if v <= 0: raise ValueError('Parameters must be positive') return v class NavierSt
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