3 problems

Let $d\geq 2$ and consider a $d$-dimensional nonlinear symmetric system that is totally linearly degenerate. Suppose the initial data belong to $H^s(\mathbb{R}^d)$ with…

Let $w$ solve the equation denoted by … lambda=1,quad 0<muleq 2,qquadtext{or}qquad lambda1,quad mu0. … will blow up in finite time for a family of smooth initial data…

For $\rho$ the density and $u=(u_r,u_\uptheta)$ the velocity solving the two-dimensional isentropic compressible Euler equations, suppose the solution constructed in Theorem genera…