Global classical solutions to 3D irrotational compressible Euler equations of Chaplygin gases with weakly decaying initial data

Abstract: We are concerned with the global classical solution problem of 3D compressible isentropic Euler equations of Chaplygin gases [ \begin{cases} \partial_tρ+ \mathrm{div}(ρv) = 0,\ \partial_t(ρv) + \mathrm{div}(ρv \otimes v) + \nabla p = 0,\ ρ(0,x) = \barρ+ \varepsilonρ0(x),\ v(0,x) = \varepsilon v_0(x). \end{cases} ] where $\barρ&gt;0$ is a constant, $\varepsilon&gt;0$ is small, the state equation is $p=p(ρ)=P_0-\frac{D}ρ$ with $P_0$ and $D$ being some positive constants. For the 3D compressible Euler equations of Chaplygin gases, which are a prototype of multidimensional nonlinear symmetric hyperbolic systems with totally linearly degenerate eigenvalues, there is a basic conjecture imposed by A. Majda: it typically has a global classical solution $(ρ, v)$ with $$(ρ-\barρ, v)\in C([0,\infty), H^s(\Bbb R³⁾⁾ \cap C^{1([0,\infty),} H^{s-1}(\Bbb R<sup>3))$$ when $(ρ_0, v_0)\in H^s(\Bbb R<sup>3)$ with $s&gt;\frac52$ unless $(ρ, v)$ itself blows up in finite time. In this paper, under the assumptions that for any fixed constant $μ$ with $0<μ<1/2$, integer $N\geq 15$, $\mathrm{rot}\,v_0(x) \equiv 0$ and [ |(ρ_0, v_0)|{H^{N}(\mathbb{R}^3)}+\sum_{|a|\leq 13} |\langle x\rangle^{1+μ} \nabla^a(ρ0,v_0)|{L^2(\mathbb{R}^3)} \leq 1, ] we show that the classical solution $(ρ, v)$ exists globally. Our main ingredients include: establishing a series of new decay estimates of energy bounds, weighted pointwise space-time $L<sup>\infty$-$L<sup>2$ estimates and weighted Strichartz-type estimates for the 3D potential flow equation of Chaplygin gases.