This paper addresses the flow of an ideal fluid in a 2D bounded domain with non-homogeneous Navier slip boundary conditions. The authors establish the solvability of the problem in the class of solutions with $L_p$-bounded vorticity, $p \in (2, \infty)$. The main result is proven by passing to the limit in the Navier-Stokes equations with vanishing viscosity. The paper is divided into several sections, including the statement of the problem, main and auxiliary results, construction of approximate solutions, and existence of a weak solution. Key concepts and definitions are introduced, and the authors provide detailed proofs for the existence of a weak solution that satisfies the Navier slip boundary condition. The paper also discusses the regularity and boundedness properties of the solutions, as well as the convergence of the approximate solutions to the exact solution as the viscosity parameter approaches zero.This paper addresses the flow of an ideal fluid in a 2D bounded domain with non-homogeneous Navier slip boundary conditions. The authors establish the solvability of the problem in the class of solutions with $L_p$-bounded vorticity, $p \in (2, \infty)$. The main result is proven by passing to the limit in the Navier-Stokes equations with vanishing viscosity. The paper is divided into several sections, including the statement of the problem, main and auxiliary results, construction of approximate solutions, and existence of a weak solution. Key concepts and definitions are introduced, and the authors provide detailed proofs for the existence of a weak solution that satisfies the Navier slip boundary condition. The paper also discusses the regularity and boundedness properties of the solutions, as well as the convergence of the approximate solutions to the exact solution as the viscosity parameter approaches zero.