Mathematical analysis of Khokhlov-Zabolotskaya-Kuznetsov KZK equationReport as inadecuate

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1 LJLL - Laboratoire Jacques-Louis Lions

Abstract : We consider the Khokhlov-Zabolotskaya-Kuznetsov KZK equation ut — uux — βuxxx— γΔy u = 0 in Sobolev spaces of functions periodic in x and with mean value zero. The derivation of KZK from the nonlinear isentropic Navier Stokes equations and the approximation of their solutions for viscous and non viscous cases, the results of the existence, uniqueness, stability and blow-up of solution of KZK equation are obtained, also a result of existence of a smooth solution of Navier-Stokes system in the half space with periodic in time mean value zero boundary conditions.

Author: Anna Rozanova-Pierrat -



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