Consider the unforced incompressible homogeneous Navier–Stokes equations on the d-
torus T^ d T d where d ≧ 4 d≥ 4 is the space dimension. It is shown that there exist …

We study the 3D hyperdissipative Navier-Stokes equations on the torus, where the viscosity
exponent α can be larger than the Lions exponent 5/4. It is well-known that, due to Lions [1] …

We consider a non-linear heat equation∂ tu= Δ u+ B (u, D u)+ P (u) posed on the d-
dimensional torus, where P is a polynomial of degree at most 3 and B is a bilinear map that …

We consider the ill-posedness issue for the cubic nonlinear heat equation and prove norm
inflation with infinite loss of regularity in the H\" older-Besov space $\mathcal C^ s= B^{s} …

We prove that there exists a nontrivial finite energy periodic stationary weak solution to the
3D Navier-Stokes equations (NSE). The construction relies on a convex integration scheme …

Considered here is the periodic initial-value problem for the regularized long-wave (BBM)
equation u t+ u x+ uux− uxxt= 0. Adding to previous work in the literature, it is shown here …

Over the centuries mathematicians have been challenged by the partial differential
equations (PDEs) that describe the motion of fluids in many physical contexts. Important and …

We prove the norm inflation phenomena for the Boussinesq system on $\mathbb T^ 3$. For
arbitrarily small initial data $(u_0,\rho_0) $ in the negative-order Besov spaces $\dot {B}^{-1} …

As an essential extension of the well known case β∈(1 2, 1] to the hyper-dissipative case
β∈(1,∞), this paper establishes both well-posedness and ill-posedness (not only norm …

WELL-POSEDNESS AND ILL-POSEDNESS FOR THE 3D GENERALIZED NAVIER-STOKES
EQUATIONS IN F Chao Deng Xiaohua Yao (Communicated by Co Page 1 DISCRETE AND …