arXiv subjects

Guirong Tang

Publications and source records attributed to Guirong Tang.

3 recordsLinked to original sources

arXiv2026

Global Dynamic Patterns of Entropy Solutions for One-dimensional Pressureless Euler System

In this paper, we are concerned with the fine properties of entropy solutions of the Cauchy problem for the one-dimensional pressureless Euler system, wherein the initial density $\rho_0$ is a locally finite Radon measure and the initial velocity $u_0\in L^\infty_{\rho_0}$. We employ the solution formula introduced by [F.M. Huang and Z. Wang, Comm. Math. Phys. 222(1) (2001), 117--146.] for this Cauchy problem to analyze the entropy solutions and obtain various new fine properties of entropy solutions; these can be summarized in four aspects: (i) Characteristics and initial waves for the Cauchy problem; (ii) Fine local structures of entropy solutions; (iii) Divides and global structures of entropy solutions; (iv) Invariants and asymptotic behaviors of entropy solutions including the asymptotic profile and the corresponding decay rates. Through these results (i)-(iv), we establish the global dynamic patterns of entropy solutions of the Cauchy problem for the $1$-D pressureless Euler system with general initial data $\rho_0$ being locally finite Radon measures and $u_0\in L^\infty_{\rho_0}$.

math.AP↗

arXiv2026

Positive-regularity norm inflation for the 3D hypodissipative Navier--Stokes equations

We prove same-space norm inflation for the three-dimensional hypodissipative Navier--Stokes equations with dissipation $(-\Delta)^\alpha$, $0<\alpha<1$. Let $2\le p<\infty$ and \[ 0<s<1-2\alpha+\frac3p. \] In the Besov case, let also $1\le q\le\infty$. There exist divergence-free $C_c^\infty(\mathbb R^3)$ initial data that are arbitrarily small in $W^{s,p}$, respectively in $B^s_{p,q}$, while the corresponding unique local smooth solution becomes arbitrarily large in the same space in arbitrarily short time. The proof adapts the anisotropic vortex-ring mixing mechanism to fractional dissipation; the strict scaling-supercritical gap makes both the curvature error and the nonlocal dissipative error perturbative.

math.AP↗

arXiv2025

Zero-relaxation and vanishing-damping limits of pressureless Euler system

We are concerned with the one-dimensional pressureless Euler system with relaxation in the Radon measure space. As the relaxation time tends to zero, the entropy solution converges to a static solution with the density converging to its initial value. As the relaxation time tends to infinity, which means the damping vanishes, the entropy solution of damped pressureless Euler system converges to that of pressureless Euler system.

math.AP↗