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We establish stability and pathwise uniqueness of solutions to Wiener noisedriven McKean-Vlasov equations with random coefficients, which are allowed tobe non-Lipschitz continuous. In the case of deterministic coefficients we alsoobtain the existence of unique strong solutions. By using our approach, whichis based on an extension of the Yamada-Watanabe ansatz to the multidimensionalsetting and which does not rely on the construction of Lyapunov functions, weprove first moment and pathwise $\alpha$-exponential stability of solutions for$\alpha > 0$. Furthermore, we are able to compute Lyapunov exponentsexplicitly.

Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach