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The incompressible impinging jet flows issuing from an asymmetric finitely long nozzle 1 1 Introduction 2 2 Statement of the physical problem and main results 3 3 Mathematical setting of the asymmetric impinging jet flow 7 3.1 Stream function formulation 8 3.2 Variational approach 9 3.3 The existence and regularity of the minimizer 11 3.4 The uniqueness and monotonicity of the minimizer 15 3.5 The free boundaries of the minimizer 18 3.6 Continuous fit condition and smooth fit condition of the free boundaries 22 4 Existence of the asymmetric impinging jet flow 24 5 Non-existence of the impinging jet flow with one asymptotic direction 28 Acknowledgments 29 References 29
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