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We develop a strategy making extensive use of tent spaces to study parabolic equa-tions with quadratic nonlinearities as for the Navier-Stokes system. We begin with a new proof of the well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in R^n with small initial data in BMO^{-1}(R^n). We then study another model where neither pointwise kernel bounds nor self-adjointness are available.
We give a new proof of a well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in $R^n$ with small initial data in $BMO^{-1}(R^n)$. The proof is formulated operator theoretically and does not make use of self-adjointness of the Laplacian.
Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); mathbf{W}^{-1,p}(Omega))$ for $p$ and $q$ in appropriate parameter ranges are proven. The case of spatially measured-valued inh
In this paper, the initial-boundary value problem of the 1D full compressible Navier-Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any $H^1$ initial data. The
In this paper, we consider the almost sure well-posedness of the Cauchy problem to the Cahn-Hilliard-Navier-Stokes equation with a randomization initial data on a torus $mathbb{T}^3$. First, we prove the local existence and uniqueness of solution. Fu
We study the Cauchy problem in $n$-dimensional space for the system of Navier-Stokes equations in critical mixed-norm Lebesgue spaces. Local well-posedness and global well-posedness of solutions are established in the class of critical mixed-norm Leb