Well-posedness for the heat flow of harmonic maps and the liquid crystals flow with rough initial data

Abstract

We investigate the well-posedness of (i) the heat flow of harmonic maps from $R^n$ to a compact Riemannian manifold without boundary for initial data in BMO; and (ii) the hydrodynamic flow $(u,d)$ of nematic liquid crystals on ${\mathbb{R}}^n$ for initial data in $BM{O}^{-1}\times BMO$.

19 pages

Cited by in corpus (25)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Regularity and existence of global solutions to the Ericksen-Leslie system in ${\mathbb{R}}^2$
• On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain
• Well-posedness of the Ericksen-Leslie system
• Global solution to the three-dimensional compressible flow of liquid crystals
• Well-Posedness of Nematic Liquid Crystal Flow in $L_{uloc}^3({\mathbb{R}}^3)$
• Finite time singularity of the nematic liquid crystal flow in dimension three
• Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows
• On the stability of type II blowup for the 1-corotational energy supercritical harmonic heat flow
• Well-posedness of the Ericksen-Leslie System for the Oseen-Frank Model in L^3_{uloc}(\mathbb{R}^3)
• On a family of exact solutions to the incompressible liquid crystals in two dimensions
• Recent results for the Landau-Lifshitz equation
• Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in ${\mathbb{R}}^3$
• Convergence of the Ginzburg-Landau approximation for the Ericksen-Leslie system
• Long-time dynamics of the nonhomogeneous incompressible flow of nematic liquid crystals
• Global existence of weak solution for the 2-D Ericksen-Leslie system
• Some remarks on the regularity of weak solutions for the stationary Ericksen-Leslie and MHD systems
• Nematic liquid crystals: Ericksen-Leslie theory with general stress tensors
• The Optimal Decay Rate of Strong Solution for the Compressible Nematic Liquid Crystal Equations with Large Initial Data
• Time decay rate of global strong solutions to nematic liquid crystal flows in ${\mathbb{R}}_{+}^3$
• Existence and large time behavior to the nematic liquid crystal equations in Besov-Morrey spaces
• The semilinear heat inequality with Morrey initial data on Riemannian manifolds
• On the regularity of very weak solutions for an elliptic coupled system of liquid crystal flows
• Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
• BKM's criterion for the 3D nematic liquid crystal flows via two velocity components and molecular orientations