Geodesic
Hyperbolic Navier-stokes equations in three space dimensions
Filomat, Tome 37 (2023) no. 7, p. 2209

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DOI

We consider in this paper a hyperbolic quasilinear version of the Navier-Stokes equations in three space dimensions, obtained by using Cattaneo type law instead of a Fourier law. In our earlier work [2], we proved the global existence and uniqueness of solutions for initial data small enough in the space H 4 (R 3) 3 × H 3 (R 3) 3. In this paper, we refine our previous result in [2], we establish the existence under a significantly lower regularity. We first prove the local existence and uniqueness of solution, for initial data in the space H 5 2 +δ (R 3) 3 × H 3 2 +δ (R 3) 3 , δ > 0. Under weaker smallness assumptions on the initial data and the forcing term, we prove the global existence of solutions. Finally, we show that if ε is close to 0, then the solution of the perturbed equation is close to the solution of the classical Navier-Stokes equations.
DOI : 10.2298/FIL2307209A
Classification : 35Q30, 76D05, 35L72
Keywords: Navier-Stokes equations, global existence, uniqueness, energy estimate, quasilinear hyperbolic equations, incompressible fluid 
Bouthaina Abdelhedi. Hyperbolic Navier-stokes equations in three space dimensions. Filomat, Tome 37 (2023) no. 7, p. 2209 . doi: 10.2298/FIL2307209A
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     title = {Hyperbolic {Navier-stokes} equations in three space dimensions},
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     year = {2023},
     volume = {37},
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     doi = {10.2298/FIL2307209A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2307209A/}
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