We present the deep random vortex network (DRVN), a novel physics-informed framework
for simulating and inferring the fluid dynamics governed by the incompressible Navier …

We prove the existence of inertial manifolds for the incompressible hyperviscous Navier–
Stokes equations on the two or three-dimensional torus:{u t+ ν (− Δ) β u+(u⋅∇) u+∇ p= f,(t …

This study proposed a new scheme called the Hermite wavelet method (HWM) to find the
numerical solutions to the multidimensional fractional coupled Navier–Stokes equation …

In this paper, we study a Navier-Stokes delay differential inclusion with time fractional
derivative of order α∈(0, 1). We first prove the local and global existence, decay and …

We propose a structure-preserving scheme and its error analysis for time-fractional Navier–
Stokes equations (TFNSEs) with periodic boundary conditions. The equations are first …

On the one hand, the primitive three-dimensional viscous equations for large-scale ocean
and atmosphere dynamics are commonly used in weather and climate predictions. On the …

In this paper, we present the result of maximum regularity of the mild solution of the fractional
Cauchy problem. As our main result, we investigate the uniqueness of mild solutions for time …

An approach to solvability of certain quasilinear parabolic equations is presented by
approximating the quasilinear equation under consideration with a parameter family of …

This self-contained book covers the theory of semilinear equations with sectorial operator
going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays …

Our purpose is to formulate an abstract result, motivated by the recent paper [8], allowing to
treat the solutions of critical and super-critical equations as limits of solutions to their …