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We investigate the problem of classification of solutions for the steadyNavier-Stokes equations in any cone-like domains. In the form of separatedvariables, $$u(x,y)=\left(  \begin{array}{c}  \varphi_1(r)v_1(\theta)  \varphi_2(r)v_2(\theta)  \end{array}  \right) ,$$ where $x=r\cos\theta$ and $y=r\sin\theta$ in polar coordinates,we obtain the expressions of all smooth solutions with $C^0$ Dirichlet boundarycondition. In particular, it shows that (i) some solutions are found, which areH\"{o}lder continuous on the boundary, but their gradients blow up at thecorner; (ii) all solutions in the entire plane of $\mathbb{R}^2$ like harmonicfunctions or Stokes equations, are polynomial expressions.

Classification of solutions of the 2D steady Navier-Stokes equations with separated variables in cone-like domains