相关论文: Prescribing a fourth order conformal invariant on …

In the first part of the paper, we give an explicit algorithm to compute the (genus zero) Gromov-Witten invariants of blow-ups of an arbitrary convex projective variety in some points if one knows the Gromov-Witten invariants of the…

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable…

This paper is devoted to establishing the compactness and existence results of the solutions to the prescribing fractional $Q$-curvatures problem of order $2\sigma$ on $n$-dimensional standard sphere when $ n-2\sigma=2$, $\sigma=1+m/2,$…

We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds…

In this paper, we study the following Lane-Emden system with nearly critical non-power nonlinearity \begin{eqnarray*} \left\{ \arraycolsep=1.5pt \begin{array}{lll} -\Delta u =\frac{|v|^{p-1}v}{[\ln(e+|v|)]^\epsilon}\ \ &{\rm in}\ \Omega,…

In \cite{JB1}, Benameur proved a blow-up result of the non regular solution of $(NSE)$ in the Sobolev-Gevrey spaces. In this paper we improve this result, precisely we give an exponential type explosion in Sobolev-Gevrey spaces with less…

In this article we are concerned with the existence of blow-up solutions to the following boundary value problem $$-\Delta v= \lambda V(x) |x|^2e^v\;\mbox{in}\quad B_1,\quad v=0 \;\mbox{ on }\quad \partial B_1,$$ where $B_1$ is the unit…

The conformal anomaly is computed on even $d$--spheres for a $p$--form propagating according to the Branson--Gover higher derivative, conformally covariant operators. The system is set up on a $q$--deformed sphere and the conformal anomaly…

In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper…

We consider the blow-up problem for discretized scale-invariant nonlinear dissipative wave equations. It is known that the critical exponents for undiscretized equations (continuous equations) are given by Fujita and Strauss exponents…

We consider a blow-up solution for a strongly perturbed semilinear heat equation with Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for the problem. Using this…

We establish theorems on the existence and compactness of solutions to the $\sigma_2$-Nirenberg problem on the standard sphere $\mathbb S^2$. A first significant ingredient, a Liouville type theorem for the associated fully nonlinear…

In this paper, we deal with the existence and multiplicity of solutions for the fractional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the…

In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr\" odinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic NLS due to Boulenger and…

We consider the problem v_t & = \Delta v+ |v|^{p-1}v \quad\hbox{in }\ \Omega\times (0, T), v & =0 \quad\hbox{on } \partial \Omega\times (0, T ) , v& >0 \quad\hbox{in }\ \Omega\times (0, T) . In a domain $\Omega\subset \mathbb R^d$, $d\ge 7$…

In this paper we study some nonlinear elliptic equations in $\R^n$ obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$ (-\Delta)^s u = \epsilon\,h\,u^q + u^p \ {{in}}\R^n,$$ where $s\in(0,1)$,…

It is still not known whether a solution to the incompressible Euler equation, endowed with a smooth initial value, can blow-up in finite time. In [{\em Comm. Math. Phys.}, 378:557--568, 2020] it has been shown that, if it exists, such a…

In this paper, we prove the soliton resolution conjecture for general type II solutions to the focusing energy critical wave equation, in space dimension 3,4 or 5, along a sequence of times. This is an important step towards the full…

We consider the semilinear wave equation with power nonlinearity in one space dimension. Given a blow-up solution with a characteristic point, we refine the blow-up behavior first derived by Merle and Zaag. We also refine the geometry of…

This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…