WELL-POSEDNESS AND ATTRACTOR FOR THE MULTI-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH FRACTIONAL DISSIPATION AND DAMPING

doi:10.1007/s10473-026-0114-5

Abstract

Abstract: The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domain $\Omega = [-\pi,\pi]^n$. Initially, we show the existence and uniqueness of strong solutions. Subsequently, we verify the continuity of the associated semigroup when $\max \{ \frac{2n+1}{n-1}, \frac{5n+2}{3n-2} \} < \beta < \frac{3n+2}{n-2}$. Finally, we establish the existence of both $H^{\alpha}$-global attractor and $H^{2\alpha}$-global attractor.

Key words: Navier-Stokes equation, global attractor, damping, strong solution

CLC Number:

35B40

Subha PAL. WELL-POSEDNESS AND ATTRACTOR FOR THE MULTI-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH FRACTIONAL DISSIPATION AND DAMPING[J].Acta mathematica scientia,Series B, 2026, 46(1): 243-254.

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