## Results on existence for generalized $$nD$$ Navier-Stokes equations.(English)Zbl 1440.35250

Summary: In this paper we consider a class of $$nD$$ Navier-Stokes equations of Kirchhoff type and prove the global existence of solutions by using a new approach introduced in [R. Jday et al., Rocky Mt. J. Math. 49, No. 5, 1595–1615 (2019; Zbl 1428.35296)].

### MSC:

 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35B65 Smoothness and regularity of solutions to PDEs 35K55 Nonlinear parabolic equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence

### Keywords:

Navier-Stokes equations; Kirchhoff; global existence

Zbl 1428.35296
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